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Real networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify vital nodes is thus very significant, allowing us to control the outbreak of epidemics, to conduct advertisements for e-commercial products, to predict popular scientific publications, and so on. The vital nodes identification attracts increasing attentions from both computer science and physical societies, with algorithms ranging from simply counting the immediate neighbors to complicated machine learning and message passing approaches. In this review, we clarify the concepts and metrics, classify the problems and methods, as well as review the important progresses and describe the state of the art. Furthermore, we provide extensive empirical analyses to compare well-known methods on disparate real networks, and highlight the future directions. In despite of the emphasis on physics-rooted approaches, the unification of the language and comparison with cross-domain methods would trigger interdisciplinary solutions in the near future.

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... 12 Among the vast set of structural measures of complex networks considered by the scientific community, centrality measures play a crucial role since they quantify the relevance of the nodes in the structure and dynamics on complex networks. 6,13 There is no consensus about a single centrality measure that resumes the relevance of each node, and therefore, there are many complementary measures that quantify different aspects of the role of each node, such as the degree, the eigenvector centrality, PageRank, HITS-Authority score, betweenness centrality, among many others. [6][7][8]13 It is natural considering the control problem related to centrality measures, that is, given a complex network = ( , ) and a centrality measure c ∶ → R, we want to modify in order to get its centrality measure c() at our wish. ...

... 6,13 There is no consensus about a single centrality measure that resumes the relevance of each node, and therefore, there are many complementary measures that quantify different aspects of the role of each node, such as the degree, the eigenvector centrality, PageRank, HITS-Authority score, betweenness centrality, among many others. [6][7][8]13 It is natural considering the control problem related to centrality measures, that is, given a complex network = ( , ) and a centrality measure c ∶ → R, we want to modify in order to get its centrality measure c() at our wish. This problem was considered for the eigenvector centrality 14,15 of weighted networks by V. Nicosia et al, 12 by proving that given a weighted and strongly connected complex network = ( , ) with n ∈ N nodes, then for every vector v = (v 1 , · · · , v n ) t ∈ R n with v i ≥ 0 for all 1 ≤ i ≤ n and v 1 + · · · + v n = 1, we can modify the weights in in order to get that its eigenvector centrality is v. ...

... As we pointed out in Section 1, there is no consensus about a single centrality measure that resumes the relevance of each node, and therefore, there are many complementary measures that quantify different aspects of the role of each node, such as the degree, the eigenvector centrality, PageRank, HITS-Authority score, betweenness centrality, among many others. [6][7][8]13 In this paper, we will consider two (spectral) centrality measures that are related with the eigenvectors of some matrices related with the graph (mainly the adjancency matrix an some of its renormalizations): the eigenvector centrality 14,15 and the (classic) PageRank centrality. 17 Eigenvector centrality was introduced by P. Bonacich 14,15 in social network analysis by considering that an individual's centrality must be a function of the centrality of those to whom he or she is connected, so the definition is related with a positive eigenvector of the transposed of the adjacency matrix as follows: ...

In this paper, some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered. We show that for every possible ranking, eventually with ties, an unweighted directed/undirected complex network can be found whose PageRank or eigenvector centrality gives the ranking considered. Different families of networks are presented in order to analytically solve this problem either for directed and undirected graphs with and without loops.

... Identifying influencers from a social network has been a fundamental research task in the web and network science research communities (Lü et al. 2016;Li et al. 2018;Morone and Makse 2015;Al-Garadi et al. 2018;Banerjee, Jenamani, and Pratihar 2020). It has been shown that a few individuals called influencers play an important role in triggering a large-scale cascade of information diffusion (Pei et al. 2014;Katz and Lazarsfeld 1955). ...

... Several algorithms for identifying influencers have been proposed (Lü et al. 2016;Li et al. 2018;Al-Garadi et al. 2018;Banerjee, Jenamani, and Pratihar 2020). A common approach is to calculate centrality measures of nodes in a social network and extract the nodes with high centrality as influencers (Chen et al. 2012;Lü et al. 2016; Morone and Makse 2015). ...

... Several algorithms for identifying influencers have been proposed (Lü et al. 2016;Li et al. 2018;Al-Garadi et al. 2018;Banerjee, Jenamani, and Pratihar 2020). A common approach is to calculate centrality measures of nodes in a social network and extract the nodes with high centrality as influencers (Chen et al. 2012;Lü et al. 2016; Morone and Makse 2015). Traditional centrality measures include degree (Freeman 1979), closeness (Freeman 1979), betweenness (Freeman 1979), PageRank (Brin and Page 1998), and k-core index (Seidman 1983;Dorogovtsev, Goltsev, and Mendes 2006). ...

Identifying influencers in a given social network has become an important research problem for various applications, including accelerating the spread of information in viral marketing and preventing the spread of fake news and rumors. The literature contains a rich body of studies on identifying influential source spreaders who can spread their own messages to many other nodes. In contrast, the identification of influential brokers who can spread other nodes' messages to many nodes has not been fully explored. Theoretical and empirical studies suggest that involvement of both influential source spreaders and brokers is a key to facilitating large-scale information diffusion cascades. Therefore, this paper explores ways to identify influential brokers from a given social network. By using three social media datasets, we investigate the characteristics of influential brokers by comparing them with influential source spreaders and central nodes obtained from centrality measures. Our results show that (i) most of the influential source spreaders are not influential brokers (and vice versa) and (ii) the overlap between central nodes and influential brokers is small (less than 15%) in Twitter datasets. We also tackle the problem of identifying influential brokers from centrality measures and node embeddings, and we examine the effectiveness of social network features in the broker identification task. Our results show that (iii) although a single centrality measure cannot characterize influential brokers well, prediction models using node embedding features achieve F$_1$ scores of 0.35--0.68, suggesting the effectiveness of social network features for identifying influential brokers.

... The study of the centrality measures is one of the most important topics in network science [1][2][3][4][5][6]. One of the questions that naturally arise when analysing a network is: 'Which are the central vertices in the network?' [7]. ...

... Essentially, a vertex positioned in the centre of a network has advantages over other vertices, as it is directly linked to many other vertices (has more edges) or acts as an intermediary in communicating with other vertices, either at speed (it is closer) or in the flow control with which it reaches the other vertices (it is between). Identifying these 'vital' vertices allow us to control the outbreak of epidemics, to conduct advertisements for e-commercial products, to predict popular scientific publications and so on [6]. There are a large number of centrality measures that capture the varying importance of the vertices (vertex-level measures) in a network according to some criterion, such as reachability, influence, embeddedness, control the flow of information [12]. ...

... DEGREE CENTRALITY Degree centrality of a vertex i for weighted networks (or the vertex strength) is defined as the sum of weights attached to edges connected to vertex i [30] 6 . Usually, it is formalized as: ...

Centrality measures are used in network science to assess the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality and betweenness centrality have solely assumed the edge weights to be constants. This article proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (interval-weighted networks, IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.

... So far, most known methods only use structural information 9 , which can be classified into neighborhoodbased centralities and path-based centralities roughly. Typical representatives of neighborhood-based centralities are degree centrality 10 (DC), H-index 11 and k-shell decomposition method 12 (KS). ...

... However, a significant number of experiments indicate that depending on a single characteristic of nodes to reliably identify influential spreaders is inadequate 9 . As a result, the methods integrating multi-characteristics of nodes have been proposed. ...

... Therefore, it is necessary to lower the impact of the k-shell index. Given an index, due to the (9) LGM ...

How to identify influential spreaders in complex networks is a topic of general interest in the field of network science. Therefore, it wins an increasing attention and many influential spreaders identification methods have been proposed so far. A significant number of experiments indicate that depending on a single characteristic of nodes to reliably identify influential spreaders is inadequate. As a result, a series of methods integrating multi-characteristics of nodes have been proposed. In this paper, we propose a gravity model that effectively integrates multi-characteristics of nodes. The number of neighbors, the influence of neighbors, the location of nodes, and the path information between nodes are all taken into consideration in our model. Compared with well-known state-of-the-art methods, empirical analyses of the Susceptible-Infected-Recovered (SIR) spreading dynamics on ten real networks suggest that our model generally performs best. Furthermore, the empirical results suggest that even if our model only considers the second-order neighborhood of nodes, it still performs very competitively.

... Wu et al. discovered that the rating bias mainly affected the fairness of rating systems [22]. Due to the limitation of space, not all methods are discussed here and interested readers can refer to the survey papers [23,24]. ...

... In order to effectively guarantee the fairness of the rating system, a number of researchers have proposed various methods [23,24]. They can be mainly divided into three different categories: item quality or user reputation measure methods, group division methods and methods with specific assumptions which are shown in Table 1. ...

... Reasonable ratings of items and user reputation ranking methods are significant to user decision makings in online e-commerce [23,24], which are listed in Table 1. In 2006, Laureti et al. firstly proposed an Iterative Ranking (IR) method to rank the items and users from self-consistency [25]. ...

Most complex systems are highly influenced by the dynamics of a small group of critical nodes. The fairness of online rating bipartite networks are also influenced by those spammers who disrupt the fairness of markets. However, a common flaw of most existing methods comes from non effectiveness to identify low-degree spammers because they are not statistically significant and detectable if the rating network is extreme sparse. To address this challenge, a new fundamental Framework to Identify Low-degree Spammers (FILS) is proposed to support the most significant methods including Deviation-based Ranking (DR),Iterative Group-based Ranking (IGR) and Iterative Optimization Ranking (IOR). Matrix completion technologies are applied to predict the possible missing ratings of low-degree users. Experimental study on three real data sets suggests that the performances of such three methods are significantly improved (4.76% − 17.41%, 23.69% − 67.15%, and 3.21% − 14.44%) when detecting random spammers. As for improvements on identifying malicious spammers, they are (17.33%−23.86%, 23.23%−23.56%, and 0.54% − 1.62%) respectively. This new idea will shed light on the future research to effectively identify low-degree spammers in online rating systems.

... Measure the influence of each node by conducting real-world experiments in social networks with more than millions of nodes is unfeasible because resources and time are limited. The mainstream ideology of this field is to estimate the spreading influence of nodes based on nodes' attributes and structural characteristics because it can sharply reduce the costs if the identification algorithms of spreading influence nodes are accurate (Lü et al., 2016;Liu et al., 2021). Existing literature reviews summarized the identification algorithms of spreading influence nodes with different focuses. ...

... Ren and Lü (2013) introduced more than 30 different algorithms before 2014. Lü et al. (2016) presented a survey on the identification algorithms of spreading influence nodes and performance evaluation metrics, and compared the performance of representative methods in different types of networks. Liu et al. (2021) reviewed the algorithms developed on the basis of centralities (Freeman, 1977;1978), PageRank (Brin and Page, 1998), and Hyperlink-Induced Topic Search (HITS) (Kleinberg, 1999). ...

... No single algorithm can achieve stable performance in all types of networks (Lü et al., 2016;Bucur, 2020;Namtirtha et al., 2021). An in-depth understanding of social network structural attributes that affect algorithmic performance can be considered the guide for the choice of algorithms when the accuracy and complexity have to be considered. ...

The identification of spreading influence nodes in social networks, which studies how to detect important individuals in human society, has attracted increasing attention from physical and computer science, social science and economics communities. The identification algorithms of spreading influence nodes can be used to evaluate the spreading influence, describe the node’s position, and identify interaction centralities. This review summarizes the recent progress about the identification algorithms of spreading influence nodes from the viewpoint of social networks, emphasizing the contributions from physical perspectives and approaches, including the microstructure-based algorithms, community structure-based algorithms, macrostructure-based algorithms, and machine learning-based algorithms. We introduce diffusion models and performance evaluation metrics, and outline future challenges of the identification of spreading influence nodes.

... Such metrics include node degree, betweenness, coreness and k-shell centrality, h-index, and more complex indices that have been proposed in the literature. A recent and rather a comprehensive list of such indices can be found in the review of Lü et al. (2016) and references therein. Another way of studying the epidemic spread in a population is to simulate the disease progression using compartmental models. ...

... To unravel such information, that a network can contain, one can use network metrics. Two types of metrics can be identified: the ones which characterized the node in order to evaluate the relevant ones in a network by identifying the vital nodes (Lü et al., 2016), the second one is used mainly to characterize the interactions in the network (Boccaletti et al., 2006). Depending on the context, the interpretations of such metrics can differ. ...

... Vital nodes and important nodes are the nodes with the greatest impact on the network structure (Bae and Kim, 2014;Basaras et al., 2013;Boccaletti et al., 2006;Chen et al., 2012;Hou et al., 2012;Kitsak et al., 2010;Liu et al., 2013) and they are essentially characterized by centrality measures. It characterizes the nodes which have the potential to spread the information faster and vaster such as degree, strength (Lü et al., 2016), betweenness (Barthelemy, 2004;Brandes, 2001), closeness (Freeman, 1978), eigencentrality (Bonacich and Lloyd, 2001), voterank , kshell (Kitsak et al., 2010). These centrality metrics are detailed in table 2.5. ...

Anticipating outbreaks of infectious diseases (endemic and emerging) and mit- igating their impacts are major challenges in human, animal and plant pathology. Surveillance for the detection of plant diseases and subsequent responses to limit their effects mobilize considerable human and economic resources. Many plant pathogens are airborne on both small and large spatial scales. It is therefore essential to de- velop adequate surveillance strategies (i.e. taking into account the characteristics of pathogen movement via air) to improve early detection of new airborne pathogen emergence and monitoring of endemic pathogen outbreaks.In this context, the research carried out in my thesis consists essentially in designing methods to model, estimate and characterize tropospheric contact networks (the troposphere is the lower layer of the atmosphere) and to exploit their properties to better monitor airborne plant pathogens. This research is essentially based on mathe- matical and statistical tools, on external software for reconstructing the trajectories of air masses (in this case HYSPLIT; https://ready.arl.noaa.gov/HYSPLIT.php) using massive meteorological databases, and on the compartmental modeling of epidemics, classically referred to by the acronym SIR (susceptible, infected, recovered). The soft- ware HYSPLIT is used to reconstruct in a relatively realistic way the movements of air masses and their non-stationarity in time and space, movements which are crucial for predicting the large-scale spread of microscopic airborne pathogens.In order to answer the above described problem, I develop in a first part of the thesis a generalist approach intended to model and infer a network of contact between geographical areas from a set of individuals’ trajectories. This approach is presented under a mathematical formalism within the framework of graph theory. The links between the nodes of the graph (in this case the above-mentioned geographical areas) are estimated by analyzing the passage (in the broad sense) of the trajectories through the nodes, which allows the inference of the contact network (or connectivity) as a whole. Different estimators for the links between nodes, based on different bio- physical hypotheses, are proposed. By applying the network construction approach to air mass trajectories over successive time periods, we obtain a spatio-temporal tropospheric contact network giving an estimate of the probability of connection for each pair of nodes donor-receiver over time. In addition, I propose to measure the error or uncertainty attached to the quantification of connections between nodes by considering several spatial and temporal sampling contexts. Once constructed and estimated, the network can be characterized topologically using classical graph theory statistics.In a second part of the thesis, I construct an epidemiological model conditioned by a contact network in order to evaluate various surveillance strategies. The epidemi- ological model is a dynamic spatial and compartmentalized model of the SIRS type (susceptible, infected, recovered, susceptible) which represents the propagation of a pathogen through the network, whether this network is estimated from the trajectories of air masses or obtained in another way. Then, spatio-temporal monitoring strategies, some of which depend on the contact network, are proposed and evaluated in terms of their ability to detect an outbreak of an emerging pathogen at an early stage. The objective is to determine where and when to monitor the pathogen’s host population.This work, which is based on massive meteorological data and consistent numer- ical codes, contributes to going beyond the classical paradigms of airborne plant pathogen monitoring. Moreover, it has a generic dimension that allows its application to frameworks other than plant epidemiology.

... This problem is typically NP-hard for general graphs [22] and its mathematical essence is a combinatorial optimization problem. In addition to early research based on exact combinatorial optimization methods to find an optimal network disintegration solution [23]- [25], researchers have also attempted to calculate the centrality measures of the nodes and then remove them individually, starting with the nodes with the highest centrality values, to develop a network disintegration strategy [12], [17], [26]. However, the set composed of a single important node may not be the most critical set of nodes, and with the increased availability of large-scale networks, novel heuristic or approximate algorithms have been proposed to find vital nodes in complex networks [27]- [29]. ...

... Therefore, we simultaneously consider multiple node importance criteria using rank aggregation (RA). In network science, the centrality of nodes is a common approach to assess the importance of nodes [26]. Thus, we first generate multiple node rankings based on various centrality measures. ...

We live in a hyperconnected world---connectivity that can sometimes be detrimental. Finding an optimal subset of nodes or links to disintegrate harmful networks is a fundamental problem in network science, with potential applications to anti-terrorism, epidemic control, and many other fields of study. The challenge of the network disintegration problem is to balance the effectiveness and efficiency of strategies. In this paper, we propose a cost-effective targeted enumeration method for network disintegration. The proposed approach includes two stages: searching candidate objects and identifying an optimal solution. In the first stage, we use rank aggregation to generate a comprehensive node importance ranking, upon which we identify a small-scale candidate set of nodes to remove. In the second stage, we use an enumeration method to find an optimal combination among the candidate nodes. Extensive experimental results on synthetic and real-world networks demonstrate that the proposed method achieves a satisfying trade-off between effectiveness and efficiency. The introduced two-stage targeted enumeration framework can also be applied to other computationally intractable combinational optimization problems, from team assembly, via portfolio investment, to drug design.

... Indeed, it allows conducting specific optimization tasks, such as controlling, minimizing, or maximizing a diffusion process. This issue is mainly related to centrality measures [2]. These measures extract diverse information from the network to quantify its importance. ...

... Classically, one can divide centrality measures into local or global measures [2]. Local measures such as Degree and Maximum Neighborhood Component quantify the node's importance based on its neighborhood. ...

Quantifying a node’s importance is decisive for developing efficient strategies to curb or accelerate any spreading phenomena. Centrality measures are well-known methods used to quantify the influence of nodes by extracting information from the network’s structure. The pitfall of these measures is to pinpoint nodes located in the vicinity of each other, saturating their shared zone of influence. In this paper, we propose a ranking strategy exploiting the ubiquity of the community structure in real-world networks. The proposed community-aware ranking strategy naturally selects a set of distant spreaders with the most significant influence in the networks. One can use it with any centrality measure. We investigate its effectiveness using real-world and synthetic networks with controlled parameters in a Susceptible-Infected-Recovered (SIR) diffusion model scenario. Experimental results indicate the superiority of the proposed ranking strategy over all its counterparts agnostic about the community structure. Additionally, results show that it performs better in networks with a strong community structure and a high number of communities of heterogeneous sizes.

... The key is to reach a good balance between the detection of malicious and random spammers, as well as to maintain a stable performance to deal with sparse rating networks. Due to the limitation of the space, not all papers in this direction are included and two comprehensive survey papers (Lü et al., 2016;Liao et al., 2017a) are recommended for overview and deep understanding. ...

It is crucial to identify spammers from online e-commerce platform to maintain the order of fairness. Existing methods have limitations to detect spammers if the underlying network is extreme sparse. In this paper, a novel method has been proposed to address this challenge from two folds. It is inspired by the idea that a trustworthy rater will always give a reasonable rating which has been statistically significant and locates in an interval following normal distribution. To deal with low-degree spammers with limited information, rating patterns with preference are involved as well. Such two parts lead to an Interval Division-based Ranking (IDR) method. Experimental study on challenging sparse network Amazon demonstrates that the performance gain of recall is at least 15.4%. Top 50 movies selected by IDR from Douban have a high mean value 9.552 and a low variance 0.036.

... The identification of influential nodes has received extensive attention from various fields, including information spreading [21], mining influential users in social networks [22], optimal control [23]. Therefore, many methods have been developed to mine influential nodes of complex networks [24]. For example, the effective distance has been used to quantify the dynamic interaction between network nodes, and an effective distance gravity model has also been proposed to measure the influence of nodes [25]. ...

The network of networks (NONs) is a case of multiplex networks, when mining key nodes in the network, the information between the various sub-networks needs to be considered. In this paper, a weighted information fusion (WIF) method is proposed to identify the influential nodes of NONs. We first divide NONs into many individual networks and then perform weighted fusion. In the process, relevant information of nodes is measured to construct the basic probability assignment (BPA) for every single network. Besides, by considering the topological structure of the network, the method of effective distance is used to describe the weight of each BPA. Finally, to measure the influential nodes of NONs, the information of all single networks is fused to obtain structural information of NONs through WIF method. More than that, the influential nodes of four real-world NONs (including Neuronal and Social two types) are measured by the proposed method, and the results are compared with other five methods, which shows that WIF method is effective in identifying the influence of nodes of NONs.

... However, the circle ratio judges the importance of the current node by the amount of information it brings to its neighbors, which inspires a new research idea [14]. Lu and Liao et al. summarized and sorted out the current node importance identification and ranking methods in various existing networks [15,16]. ...

Relatively important node mining has always been an essential research topic in complex networks. Existing relatively important node mining algorithms suffer from high time complexity and poor accuracy. Therefore, this paper proposes an algorithm for mining relatively important nodes based on the edge importance greedy strategy (EG). This method considers the importance of the edge to represent the degree of association between two connected nodes. Therefore, the greater the value of the connection between a node and a known important node, the more likely it is to be an important node. If the importance of the edges in an undirected network is measured, a greedy strategy can find important nodes. Compared with other relatively important node mining methods on real network data sets, such as SARS and 9/11, the experimental results show that the EG algorithm excels in both accuracy and applicability, which makes it a competitive algorithm in the mining of important nodes in a network.

... There is a great deal of literature on the identification of influential nodes within a network [28]. While some of this work is not directly related to the social media space, it offers some guidance about how nodes -in our case, accounts -interact within an information diffusion network. ...

The world's digital information ecosystem continues to struggle with the spread of misinformation. Prior work has suggested that users who consistently disseminate a disproportionate amount of low-credibility content -- so-called superspreaders -- are at the center of this problem. We quantitatively confirm this hypothesis and introduce simple metrics to predict the top misinformation superspreaders several months into the future. We then conduct a qualitative review to characterize the most prolific superspreaders and analyze their sharing behaviors. Superspreaders include pundits with large followings, low-credibility media outlets, personal accounts affiliated with those media outlets, and a range of influencers. They are primarily political in nature and use more toxic language than the typical user sharing misinformation. We also find concerning evidence suggesting that Twitter may be overlooking prominent superspreaders. We hope this work will further public understanding of bad actors and promote steps to mitigate their negative impacts on healthy digital discourse.

... D etermining the influence of nodes in networks is critical for understanding and controlling real-world systems 1 . Applications include identifying super spreaders in marketing and political campaigns 2 , immunization targets for disease containment 3 , vulnerable nodes in financial networks 4 , and key therapeutic targets in biological signaling and regulatory networks [5][6][7] . ...

The optimization problem aiming at the identification of minimal sets of nodes able to drive the dynamics of Boolean networks toward desired long-term behaviors is central for some applications, as for example the detection of key therapeutic targets to control pathways in models of biological signaling and regulatory networks. Here, we develop a method to solve such an optimization problem taking inspiration from the well-studied problem of influence maximization for spreading processes in social networks. We validate the method on small gene regulatory networks whose dynamical landscapes are known by means of brute-force analysis. We then systematically study a large collection of gene regulatory networks. We find that for about 65% of the analyzed networks, the minimal driver sets contain less than 20% of their nodes. Boolean networks modelling various biological processes are characterized by nonlinear reversible dynamics that makes their control challenging. The authors introduce extended concepts of influence and control, typically considered in the study of spreading processes, for Boolean dynamics.

... Vignery (2020) found that both a selection effect and a socialization process (peer performance) influenced student achievement; the centrality univariate effects are thus significant for student performance. Lü (2016) found that nodes with a higher degree of centrality had a greater impact. Vargas et al. (2018) found that centrality was significantly positively correlated with students' homework scores in all three courses: in-strength, out-strength, closeness centrality, and harmonic centrality. ...

Weibo, China’s largest microblogging platform, has become one of the key information-sharing platforms in modern society. This study examines topic propagation in relation to microblogging from the perspective of the “peer effect.” Using data of hot topics from Weibo, we analyze how the social effect and propagation pathway influence the topic propagation process. We propose a spatial and temporal heterogeneity diffusion model that includes endogenous and exogenous social effects and is based on but different from the Bass diffusion model. We find that most propagation pathways end after a single level of propagation. The endogenous social effect in microblogs primarily influences the inflow of topics. Such endogenous social effect, combined with the multiplier effect, motivates most users to share a microblog topic in a short period of time. The exogenous social effect primarily influences the outflow of topics, and therefore, the microblog topics of a small number of popular users’ account for most of the share volume. Our results are robust to potential serial correlation, reflection problem, and potential self-selection due to user status.
The findings reveal that group characteristics affect individuals’ behaviors and choices in relation to the topic propagation process on microblogging platforms. The use of a spatial and temporal heterogeneity diffusion model and the robustness of the analysis process provide new information for scholars in this field.

... Degree centrality, as an essential topological property, was frequently used to characterize the node importance in a network 24,25 . In this paper, we address the problem of how to choose the initial seeds for influence maximization in hypergraphs based on the node degree. ...

Influence maximization in complex networks, i.e., maximizing the size of influenced nodes via selecting K seed nodes for a given spreading process, has attracted great attention in recent years. However, the influence maximization problem in hypergraphs, in which the hyperedges are leveraged to represent the interactions among more than two nodes, is still an open question. In this paper, we propose an adaptive degree-based heuristic algorithm, i.e., Heuristic Degree Discount (HDD), which iteratively selects nodes with low influence overlap as seeds, to solve the influence maximization problem in hypergraphs. We further extend algorithms from ordinary networks as baselines and compare the performance of the proposed algorithm and baselines on both real data and synthetic hypergraphs. Results show that HDD outperforms the baselines in terms of both effectiveness and efficiency. Moreover, the experiments on synthetic hypergraphs indicate that HDD shows high performance, especially in hypergraphs with heterogeneous degree distribution.

... In the power graph, this paper uses two indexes to evaluate the importance of nodes, k i and c i , respectively. k i is the closeness centrality of node i, which is usually calculated by the node contraction method [25]. k i evaluates the importance of node i by summarizing all the distances between node i and other nodes. ...

Parallel restoration following blackouts can reduce economic and social losses. This paper aims to develop a parallel restoration method coordinating the partitioning scheme of the blackout system and restoration strategies of subsystems. The susceptible-infected-recovered model, i.e., a virus propagation model of complex networks, is used to decide the parallel restoration strategies online. Firstly, various types of viruses are used to represent different subsystems. The probability vector of virus infection is obtained according to the importance level of each bus. Secondly, an immunization strategy is developed based on the faulted buses in the blackout situation. According to the infection rate and the immunization strategy, the virus propagation direction will be changed based on real-time system conditions. The startup characteristics of units and the charging reactive power of restoration paths are considered as constraints to embed in the virus propagation process. Finally, the partitioning scheme and the restorative actions for subsystems are determined based on the infected results of viruses. The effectiveness of the proposed method is validated by case studies on the IEEE 39-bus and the IEEE 118-bus test systems.

... As one of the de facto standard measures [20], the h-index has been successfully applied to different domains [21][22][23][24]. Unfortunately, how to understand and interpret the h-index of a network node from a statistical viewpoint is still lacking. ...

Evaluating the importance of a network node is a crucial task in network science and graph data mining. H-index is a popular centrality measure for this task, however, there is still a lack of its interpretation from a rigorous statistical aspect. Here we show the statistical nature of h-index from the perspective of order statistics, and we obtain a new family of centrality indices by generalizing the h-index along this direction. The theoretical and empirical evidences show that such a statistical interpretation enables us to obtain a general and versatile framework for quantifying the importance of a network node. Under this framework, many new centrality indices can be derived and some of which can be more accurate and robust than h-index. We believe that this research opens up new avenues for developing more effective indices for node importance quantification from a viewpoint that still remains unexplored.

... RN is, in fact, a superior sampling method to RV for finding high-degree vertices and has gained popularity in many contexts and areas of research (for example, see Han et al. 2013;Lü et al. 2016;Christakis and Fowler 2010). However, there is a cost for this gain. ...

Random neighbor sampling, or RN , is a method for sampling vertices with a mean degree greater than that of the graph. Instead of naïvely sampling a vertex from a graph and retaining it (‘random vertex’ or RV ), a neighbor of the vertex is selected instead. While considerable research has analyzed various aspects of RN , the extra cost of sampling a second vertex is typically not addressed. This paper explores RN sampling from the perspective of cost. We break down the cost of sampling into two distinct costs, that of sampling a vertex and that of sampling a neighbor of an already sampled vertex, and we also include the cost of actually selecting a vertex/neighbor and retaining it for use rather than discarding it. With these three costs as our cost-model, we explore RN and compare it to RV in a more fair manner than comparisons that have been made in previous research. As we delve into costs, a number of variants to RN are introduced. These variants improve on the cost-effectiveness of RN in regard to particular costs and priorities. Our full cost-benefit analysis highlights strengths and weaknesses of the methods. We particularly focus on how our methods perform for sampling high-degree and low-degree vertices, which further enriches the understanding of the methods and how they can be practically applied. We also suggest ‘two-phase’ methods that specifically seek to cover both high-degree and low-degree vertices in separate sampling phases.

... In fact, the majority of the proposed models that identify influential nodes only the structural information, which allows the wide applications independent to the specific dynamical processes under consideration. The concept centrality was mainly proposed to answer the question that how to characterize a node's importance according to the network topology [9]. A systematic literature review should include the information about the influential authors, institutions and countries of the research area. ...

A comprehensive literature review has always been an essential first step of every meaningful research. In recent years, however, the availability of a vast amount of information in both open-access and subscription-based literature in every field has made it difficult, if not impossible, to be certain about the comprehensiveness of one's survey. This subsequently can lead to reviewers' questioning of the novelties of the research directions proposed, regardless of the quality of the actual work presented. In this situation, statistics derived from the published literature data can provide valuable quantitative and visual information about research trends, knowledge gaps, and research networks and hubs in different fields. Our tool provides an automatic and rapid way of generating insight for systematic reviews in any research area.

... Incoreness. Coreness is a widely-used metric in vital node identification studies [47,49]. The calculation of coreness is based on the well-known k-shell decomposition [50], proposed by Seidman in 1983. ...

Recent strides in economic complexity have shown that the future economic development of nations can be predicted with a single "economic fitness" variable, which captures countries' competitiveness in international trade. The predictions by this low-dimensional approach could match or even outperform predictions based on much more sophisticated methods, such as those by the International Monetary Fund (IMF). However, all prior works in economic complexity aimed to quantify countries' fitness from World Trade export data, without considering the possibility to infer countries' potential for growth from alternative sources of data. Here, motivated by the long-standing relationship between technological development and economic growth, we aim to forecast countries' growth from patent data. Specifically, we construct a citation network between countries from the European Patent Office (EPO) dataset. Initial results suggest that the H-index centrality in this network is a potential candidate to gauge national economic performance. To validate this conjecture, we construct a two-dimensional plane defined by the H-index and GDP per capita, and use a forecasting method based on dynamical systems to test the predicting accuracy of the H-index. We find that the predictions based on the H-index-GDP plane outperform the predictions by IMF by approximately 35%, and they marginally outperform those by the economic fitness extracted from trade data. Our results could inspire further attempts to identify predictors of national growth from different sources of data related to scientific and technological innovation.

... Lee et al. proposed Deviation-based Ranking (DR) [24], in which Z-score is used to measure the deviation of users. We don't discuss all reputation ranking methods here due to space limitations, but interested readers can read the survey paper [25]. At present, there are some new developments in the field of natural language processing, such as user interest mining, healthcare applications, etc. Interested readers can read the survey paper [26], [27]. ...

In the e-commerce platform, user purchase behavior often depends on personal experience and the objective ratings of others. Various businesses employ a large number of spammers to obtain illegal benefits by distorting the ranking of goods, which seriously affects the market order. How to design a high-speed and effective ranking method to remove these spammers is necessary and significant. In this paper, a novel reputation ranking method is proposed based on users' Rating Patterns and Rating Deviation (RPRD) because users' rating preference and historical behavior differ significantly with spammers. We compare RPRD method with three classical methods Deviation-based Ranking (DR), Iterative Group-based Ranking (IGR) and Iterative Balance Ranking (IBR) on three real datasets. Experimental results show that the RPRD method can effectively resist spammers attack and identification, especially in detecting random spammers. On the other hand, this method always has high accuracy and robustness even if the network is relatively sparse. It can also be applied in large and sparse bipartite rating networks in a short time.

... Other exciting hypotheses exist as well. The work by Lv et al. provided a thorough review many noteworthy applications and approaches of reputation-based ranking methods [24], which is highly recommended to read. ...

With the rapid development of e-commerce in recent years, a large number of spammers disrupt the fair order of the e-commerce platform. The false ratings rated by these spammers do not match the quality of items, confusing the boundaries of good and bad items and seriously endangering the real interests of merchants and normal users. In order to eliminate the malicious influence caused by these spammers, many effective spamming detection algorithms are proposed in e-commerce platforms. However, these algorithms are ineffective in judging how trustworthy a user with insufficient rating data. In order to address this issue, we take inspiration from traditional recommender systems by completing the missing ratings of low-degree users to improve the efficiency of spamming detection algorithms when approaching those users. User similarity is used in this paper to predict the missing ratings of users. A new reputation ranking method IOR_LU is proposed. We then test our improvements compared with DR, IGR, and IOR. Experimental results on three typical data sets show that our method combined with IOR has improved by at least 9.68%, 3.29%, and 0.21% in dealing with malicious spammers, respectively. As for results on detecting random spammers, our method improves by a least 5.06%, 21.12% and 4.46%, respectively.

... These nodes are called superspreaders [8], influencers [4], influential spreaders [9], or influential nodes [10]. Finding influential nodes has an important impact on many issues related to spreading processes, such as innovation diffusion [11], viral marketing [12], decision making [13], predicting popular scientific publications [14], and so on. Therefore, identifying influential nodes is of practical significance and has attracted extensive attention from scholars. ...

Identifying the most influential spreaders in online social networks plays a prominent role in affecting information dissemination and public opinions. Researchers propose many effective identification methods, such as k-shell. However, these methods are usually validated by simulat- ing propagation models, such as epidemic-like models, which rarely consider the Push-Republish mechanism with attenuation characteristic, the unique and widely-existing spreading mechanism in online social media. To address this issue, we first adopt the Push-Republish (PR) model as the underlying spreading process to check the performance of identification methods. Then, we find that the performance of classical identification methods significantly decreases in the PR model compared to epidemic-like models, especially when identifying the top 10% of superspreaders. Furthermore, inspired by the local tree-like structure caused by the PR model, we propose a new identification method, namely the Local-Forest (LF) method, and conduct extensive experiments in four real large networks to evaluate it. Results highlight that the Local-Forest method has the best performance in accurately identifying superspreaders compared with the classical methods.

... ic centrality indices only capture interconnectedness among stock markets, i.e., indegree (ID), outdegree (OD), closeness centrality (CLO), betweenness centrality (BTW), and clustering coefficient (CLU). The descriptions and formulations of the indices have been comprehensively introduced in the related references (León, Machado, & Sarmiento, 2018;L. Y. Lu et al., 2016;Wang, Gao, et al., 2020). ...

Measuring the systemic risk contribution (SRC) of country-level stock markets helps understand the rise of extreme risks in the worldwide stock system to prevent potential financial crises. This paper proposes a novel SRC measurement based on quantifying tail risk propagation's domino effect using ΔCoVaR and the cascading failure network model. While ΔCoVaR captures the tail dependency structure among stock markets, the cascading failure network model captures the nonlinear dynamic characteristics of tail risk contagion to mimic tail risk propagation. As an illustration, we analyze 73 markets' SRCs using a daily closing price dataset from 1990.12.19 to 2020.9.8. The validity test demonstrates that our method outperforms seven classic methods as it helps early warning global financial crises and correlates to many systemic risk determinants, e.g., the market liquidity, leverage, inflation, and fluctuation. The empirical results identify that Southeast European markets have higher SRCs with time-varying and momentum features corresponding to significant financial crisis events. Besides, it needs attention that South American and African markets have displayed increasing risk contributions since 2018. Overall, our results highlight that considering tail risk contagion's dynamic characteristics helps avoid underestimating SRC and supplement a “too cascading impactive to fail” perspective to improve financial crisis prevention.

... SIR model is a classical model to describe the mechanism of information diffusion. It can not only study the dynamics diffusion process but also position the key nodes and analyze the threshold of virus propagation [14][15][16][17]. The diffusion characteristics of computer network viruses are similar to those of biological viruses, which are latent, infectious, and destructive; thus, the evolution of virus infection among network nodes can be considered, and the SIR model is used to analyze the computer virus diffusion [18][19][20][21][22]. SIR model is introduced to study the mechanism of hacker intrusion diffusion, which has certain innovative significance. ...

The spread of network attacks is extremely harmful, which poses a great threat to the assets and reputation of firms. Therefore, making a scientific information security strategy is an important task for the continued and stable development of the firms. This paper develops the SIR model of hacker intrusion propagation and then analyzes the evolution trend of hacker intrusion propagation and the conditions of strategy transfer. The research shows that when immune failure and strategy transfer are not considered, the threshold of hacker intrusion propagation is negatively correlated with the probability of invasion, whereas it is positively correlated with the probability of defense success and the externality during outsourcing. In the case of immune failure, there will always be infected firms in the network, where the threshold of hacker intrusion propagation is affected by the proportion of the infected state and the probability of immune failure. When immune failure and strategy transfer occur simultaneously if the externality is positive and high, information security outsourcing can improve firms’ security benefits; if the externality is negative, the firms should stop cooperating with the managed security service provider (MSSP).

... Simple mathematical models that capture the fundamentals of epidemic spread can be used to fit data using a large number of parameters, and the resulting values can be used to generate accurate forecasts. In recent years, the scientific community has gathered significant justification for diverse and complex social network connection patterns [15], [16]. ...

The novel coronavirus (nCOV) is a new strain that needs to be hindered from spreading by taking effective preventive measures as swiftly as possible. Timely forecasting of COVID-19 cases can ultimately support in making significant decisions and planning for implementing preventive measures. In this study, three common machine learning (ML) approaches via linear regression (LR), sequential minimal optimization (SMO) regression, and M5P techniques have been discussed and implemented for forecasting novel coronavirus disease-2019 (COVID-19) pandemic scenarios. To demonstrate the forecast accuracy of the aforementioned ML approaches, a preliminary sample-study has been conducted on the first wave of the COVID-19 pandemic scenario for three different countries including the United States of America (USA), Italy, and Australia. Furthermore, the contributions of this study are extended by conducting an in-depth forecast study on COVID-19 pandemic scenarios for the first, second, and third waves in India. An accurate forecasting model has been proposed, which has been constructed on the basis of the results of the aforementioned forecasting models of COVID-19 pandemic scenarios. The findings of the research highlight that LR is a potential approach that outperforms all other forecasting models tested herein in the present COVID-19 pandemic scenario. Finally, the LR approach has been used to forecast the likely onset of the fourth wave of COVID-19 in India.

Recent strides in economic complexity have shown that the future economic development of nations can be predicted with a single “economic fitness” variable, which captures countries' competitiveness in international trade. The predictions by this low-dimensional approach could match or even outperform predictions based on much more sophisticated methods, such as those by the International Monetary Fund (IMF). However, all prior works in economic complexity aimed to quantify countries' fitness from World Trade export data, without considering the possibility to infer countries' potential for growth from alternative sources of data. Here, motivated by the long-standing relationship between technological development and economic growth, we aim to forecast countries' growth from patent data. Specifically, we construct a citation network between countries from the European Patent Office (EPO) dataset. Initial results suggest that the H-index centrality in this network is a potential candidate to gauge national economic performance. To validate this conjecture, we construct a two-dimensional plane defined by the H-index and GDP per capita, and use a forecasting method based on dynamical systems to test the predicting accuracy of the H-index. We find that the predictions based on the H-index-GDP plane outperform the predictions by IMF by approximately 35%, and they marginally outperform those by the economic fitness extracted from trade data. Our results could inspire further attempts to identify predictors of national growth from different sources of data related to scientific and technological innovation.

In the information spreading mechanism of social networks, the influence propagation of information sources often has different effects on different users. How to effectively suppress the negative effects is particularly important. In the case of unknown network propagation principle, this paper introduces the idea of swarm intelligence, which utilizes the positive feedback mechanism of ant colony to simulate the propagation of negative influence, and finds a set of high-value and low-cost suppression nodes. On this basis, the graph embedding technique is used to obtain the new relationships between nodes in the network, and the new relationships between the nodes are used as heuristic information for the ant colony algorithm. Experiments show that our algorithm can not only find the set of inhibitory nodes with limited cost, but also effectively limit the spread of negative influence in the network compared with other algorithms. The research of this paper can not only enrich the theoretical research results of influence maximization, but also play an important role in the analysis of network topology, as well as in the fields of epidemic prevention and control, rumor propagation and so on.

“Made in China” has spread all over the world, and China has the status of “world factory”. However, the weak ability of independent innovation has affected the sustainable development of China’s manufacturing industry. The industrial revolution with digital and intelligent manufacturing as the core is coming. In the future, our development is not fast, and the key is how to be sustainable and healthy. The development of zero carbon vehicles such as intelligent transportation and electric vehicles is one of the highlands of technological competition in the transportation field, and it is also the core measure to achieve carbon peak and carbon neutralization. Identifying important firms in the automobile industry has always been a topical issue. This study used the transaction data of listed companies in China’s automobile manufacturing industry to build a complex network based on the quantitative data of enterprise development status using network modeling and the multi-attribute decision evaluation method. The relationship between the network structure of the financial market and the multi-index sustainability evaluation of enterprises were also studied. By extracting the financial information of environmental protection investment from the social responsibility reports of listed companies and analyzing the current status of target investment in the automobile manufacturing industry, the research shows that the current environmental protection investment in the automobile manufacturing industry is not strong and the government needs to increase supervision. The finding reveals three dynamic relationships for practical impact. The empirical result verifies that our method is effective and reliable. This approach can effectively overcome the effect of subjective factors on evaluation and provide sustainable evaluation strategy suggestions for investors in the automobile manufacturing industry.

Air traffic systems are of great significance to our society. However, air traffic systems are extremely complicated since an air traffic system encompasses many components which could evolve over time. It is therefore challenging to analyze the evolution dynamics of air traffic systems. In this paper we propose a graph perspective to trace the spatial‐temporal evolutions of air traffic systems. Different to existing studies which are model‐driven and only focus on certain properties of an air traffic system, in this paper we propose a data‐driven perspective and analyze a couple of properties of an air traffic system. Specifically, we model air traffic systems with both unweighted and weighted graphs with respect to real‐world traffic data. We then analyze the evolution dynamics of the constructed graphs in terms of nodal degrees, degree distributions, traffic delays, causality between graph structures and traffic delays, and system resilience under airport failures. To validate the effectiveness of the proposed approach, a case study on the American air traffic systems with respect to 12‐month traffic data is carried out. It is found that the structures and traffic mobilities of the American air traffic systems do not evolve significantly over time, which leads to the stable distributions of the traffic delays as evidenced by a causality analysis. It is further found that the American air traffic systems are quite robust to random airport failures while, respectively, 20% and 10% failures of the hub airports will lead to the collapse of the entire system with respect to the two proposed cascading failure models.

Due to the continuous emergence of various social and trade networks, network influence analysis has aroused great interest of the researchers. Based on different influence propagation models, many new models and methods for influence maximization on networks have been proposed. As an extension and expansion of the traditional influence maximization problem, influence blocking maximization has become a hotspot of research, and has been widely applied in many areas such as physics, computer science and epidemiology. In recent years, various methods for influence blocking maximization problem have been reported. However, we still lack a comprehensive review to systematically analyze the methodological and theoretical advances in influence blocking maximization problem from the aspects of social networks influence analysis. This review aims to fill this gap by providing a comprehensive survey and analysis of the theory and applications of influence blocking maximization. Not only it advances the theoretical understanding of the influence maximization problem, but will be a point of reference for future researches.

Large networks are quintessential to bioinformatics, knowledge graphs, social network analysis, and graph-based learning. CompositeView is a Python-based open-source application that improves interactive complex network visualization and extraction of actionable insight. CompositeView utilizes specifically formatted input data to calculate composite scores and display them using the Cytoscape component of Dash. Composite scores are defined representations of smaller sets of conceptually similar data that, when combined, generate a single score to reduce information overload. Visualized interactive results are user-refined via filtering elements such as node value and edge weight sliders and graph manipulation options (e.g., node color and layout spread). The primary difference between CompositeView and other network visualization tools is its ability to auto-calculate and auto-update composite scores as the user interactively filters or aggregates data. CompositeView was developed to visualize network relevance rankings, but it performs well with non-network data. Three disparate CompositeView use cases are shown: relevance rankings from SemNet 2.0, an open-source knowledge graph relationship ranking software for biomedical literature-based discovery; Human Development Index (HDI) data; and the Framingham cardiovascular study. CompositeView was stress tested to construct reference benchmarks that define breadth and size of data effectively visualized. Finally, CompositeView is compared to Excel, Tableau, Cytoscape, neo4j, NodeXL, and Gephi.

In this paper, we investigate the problem of influence seeding strategy in multilayer networks. In consideration of the fact that there exist inter-layer conversion costs associated with influence diffusion between layers in multiplex networks, a novel two-step seeding strategy is proposed to identify influential individuals in multiplex networks. The first step is to determine the target layer, and the second step is to identify the target seeds. Specifically, we first propose two comparable layer selection strategies, namely, multiplex betweenness centrality and multi-hop multiplex neighbors (MMNs), to determine the target layer of seeding diffusion and then construct a multiplex gravity centrality (MGC) in the manner of the gravity model to identify the influential seeds in the target layer. Subsequently, we employ a redefined independent cascade model to evaluate the effectiveness of our proposed seeding strategy by comparing it with other commonly used centrality indicators, which is validated on both synthetic and real-world network datasets. The experimental results indicate that our proposed seeding strategy can obtain greater influence coverage. In addition, parameter analysis of a neighborhood range demonstrates that MMN-based target layer selection is relatively robust, and a smaller value of a neighborhood range can enable MGC to achieve better influence performance.

Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures which go beyond a simple collection of dyadic interactions has rendered them void of performance guarantees. We here introduce a new measure of node's centrality, which is no longer a scalar value, but a vector with dimension one lower than the highest order of interaction in a hypergraph. Such a vectorial measure is linked to the eigenvector centrality for networks containing only dyadic interactions, but it has a significant added value in all other situations where interactions occur at higher-orders. In particular, it is able to unveil different roles which may be played by the same node at different orders of interactions – information that is otherwise impossible to retrieve by single scalar measures. We demonstrate the efficacy of our measure with applications to synthetic networks and to three real world hypergraphs, and compare our results with those obtained by applying other scalar measures of centrality proposed in the literature.

We study influence maximization on temporal networks. This is a special setting where the influence function is not submodular, and there is no optimality guarantee for solutions achieved via greedy optimization. We perform an exhaustive analysis on both real and synthetic networks. We show that the influence function of randomly sampled sets of seeds often violates the necessary conditions for submodularity. However, when sets of seeds are selected according to the greedy optimization strategy, the influence function behaves effectively as a submodular function. Specifically, violations of the necessary conditions for submodularity are never observed in real networks, and only rarely in synthetic ones. The direct comparison with exact solutions obtained via brute-force search indicates that the greedy strategy provides approximate solutions that are well within the optimality gap guaranteed for strictly submodular functions. Greedy optimization appears, therefore, to be an effective strategy for the maximization of influence on temporal networks.

Understanding the high-tech industrial agglomeration from a spatial-spillover perspective is essential for cities to gain economic and technological competitive advantages. Along with rapid urbanization and the development of fast transportation networks, socioeconomic interactions between cities have been ever-increasing, traditional spatial metrics are not enough to describe actual inter-city connections. High-skilled labor flow between cities strongly influences the high-tech industrial agglomeration, yet receives less attention. By exploiting unique large-scale datasets and tools from complex network and data mining, the authors construct an inter-city high-skilled labor flow network, which was integrated into spatial econometric models. The regression results indicate that spatial-spillover effects exist in the development of high-tech industries in the Yangtze River Delta Urban Agglomeration region. Moreover, the spatial-spillover effects are stronger among cities with a higher volume of high-skilled labor flows than among cities with just stronger geographic connections. Additionally, the authors investigate the channels for the spillover effects and discover that inadequate local government expenses on science and technology likely hamper the high-tech industrial agglomeration, so does the inadequate local educational provision. The increasing foreign direct investments in one city likely encourages the high-tech industrial agglomeration in other cities because of the policy inertia toward traditional industries.

The problem of influence maximization in social networks has attracted much attention, and some algorithms have been proposed. However, the existing methods may be not suitable for large-scale networks because of high time complexity or failing to achieve the great performance. Given that the impacts of seeds in the loose neighbors (i.e., only including one-hop path with the candidate node) and the close neighbors (i.e., including one-hop and two-hop paths with the candidate node, and they form a closed triad) on the degree discount of candidate node are different. Moreover, when selecting multiple nodes as the seeds, we should not only consider the importance of the seeds themselves, but also ensure that the seeds are sufficiently dispersed to avoid the redundancy of propagation. To the end, we propose an efficient heuristic algorithm for influence maximization in social networks by considering redundancy weakening and two types of seeds into degree discount (named RWTDD). Based on the independent cascade model, the proposed RWTDD is compared with some well-known heuristic algorithms and greedy algorithms in six real social networks, experimental results indicate that the proposed RWTDD has a better influence coverage and low time complexity.

Diverse real world systems can be abstracted as complex networks consisting of nodes and edges as functional components. Percolation theory has shown that the failure of a few of nodes could lead to the collapse of a whole network, which brings up the network dismantling problem: How to select the least number of nodes to decompose a network into disconnected components each smaller than a predefined threshold? For its NP-hardness, many heuristic approaches have been proposed to measure and rank each node according to its importance to network structural stability. However, these measures are from a uniscale viewpoint by regarding one complex network as a flatted topology. In this article, we argue that nodes’ structural importance can be measured in different scales of network topologies. Built upon recent deep learning techniques, we propose a self-supervised learning based network dismantling framework (NEES), which can hierarchically merge some compact substructures to convert a network into a coarser one with fewer nodes and edges. During the merging process, we design neural models to extract essential structures and utilize self-attention mechanisms to learn nodes’ importance hierarchy in each scale. Experiments on real world networks and synthetic model networks show that the proposed NEES outperforms the state-of-the-art schemes in most cases in terms of removing the least number of target nodes to dismantle a network. The dismantling effectiveness of our neural extraction framework also highlights the emerging role of multi-scale essential structures.

In modern systems, from brain neural networks to social group networks, pairwise interactions are not sufficient to express higher-order relationships. The smallest unit of their internal function is not composed of a single functional node but results from multiple functional nodes acting together. Therefore, researchers adopt the hypergraph to describe complex systems. The targeted attack on random hypergraph networks is still a problem worthy of study. This work puts forward a theoretical framework to analyze the robustness of random hypergraph networks under the background of a targeted attack on nodes with high or low hyperdegrees. We discovered the process of cascading failures and the giant connected cluster (GCC) of the hypergraph network under targeted attack by associating the simple mapping of the factor graph with the hypergraph and using percolation theory and generating function. On random hypergraph networks, we do Monte-Carlo simulations and find that the theoretical findings match the simulation results. Similarly, targeted attacks are more effective than random failures in disintegrating random hypergraph networks. The threshold of the hypergraph network grows as the probability of high hyperdegree nodes being deleted increases, indicating that the network’s resilience becomes more fragile. When considering real-world scenarios, our conclusions are validated by real-world hypergraph networks. These findings will help us understand the impact of the hypergraph’s underlying structure on network resilience.

El proyecto “Reconstruyendo la historia desde adentro - Una experiencia significativa en la Ciudad de Pereira, Risaralda: San Isidro, Puerto Caldas” fue una apuesta del Semillero de
Investigación “Familia, Educación y Comunidad” adscrito al Grupo de Investigación “Educación y Desarrollo Humano”, realizado en el año 2019. Consistió en generar una articulación de tres conceptos considerados fundamentales en la formación integral como lo son: la familia, la educación y la comunidad, que en esta oportunidad se enmarcaron en la reconstrucción de la historia de vida de la comunidad de San Isidro, la cual ha sido acompañada por diversas instituciones que contemplan dentro de sus áreas de responsabilidad social el desarrollo comunitario.

The current level of development of online social networks has transformed social media from a way of communication between people into a tool for influencing people’s behaviour in their daily lives. This influence is often aimed at inciting protest movements in society and mobilising citizens for protest actions, and has a targeted impact on social network users. The sponsors and main actors of disruptive influences are often forces located in other countries. In the context of counteraction to targeted destructive influences, the task of identifying the network structure of destructive influence is very relevant. One element of this structure is the users connecting individual communities to the core of the protest network. These users are the bridges between the clusters and the core network. Their main task is to contribute to the rapid growth of the protest audience. Identifying the most influential bridges and blocking them could decrease the protest potential or make the protest actions ineffective. In this paper, we propose a methodology for identifying bridge users based on the original centrality measure of weighted contribution. Moreover, a method for identifying the most influential bridges is proposed. Unlike most probabilistic methods, weighted contribution centrality allows for clear determination of whether a user is a bridge or not. A description of the measure, a mathematical model and an algorithm for calculating it are presented.KeywordsOnline social networksSocial network analysisStructure of protest networkCore of protest networkClustersCommunityBridgesWeighted contribution centrality

How to evaluate the importance of nodes and identify influential nodes in complex networks is a very significant research in the field of network science. Most of existing algorithms neglect the relationship between a node and its neighbors to evaluate the importance of nodes in networks. In this work, we first define nodes communication probability sequence by making use of the length and number of shortest paths between node pairs. Then the traditional binary adjacency matrix is converted into correlation matrix through relative entropy. Based on information Communication Probability and Relative entropy (CPR), an improved Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), called CPR-TOPSIS, is presented for identifying influential nodes in complex networks from the view of global, local and location information dimensions. The proposed algorithm has been compared with eight state-of-the-art algorithms on several real-world networks to verify the performance. Experimental results show that CPR-TOPSIS has better performance in terms of monotonicity, resolution, ranking accuracy, imprecision function and top-10 nodes.

Dependence can highly increase the vulnerability of interdependent networks under cascading failure. Recent studies have shown that a constant density of reinforced nodes can prevent catastrophic network collapses. However, the effect of reinforcing dependency links in interdependent networks has rarely been addressed. Here, we develop a percolation model for studying interdependent networks by introducing a fraction of reinforced dependency links. We find that there is a minimum fraction of dependency links that need to be reinforced to prevent the network from abrupt transition, and it can serve as the boundary value to distinguish between the first- and second-order phase transitions of the network. We give both analytical and numerical solutions to the minimum fraction of reinforced dependency links for random and scale-free networks. Interestingly, it is found that the upper bound of this fraction is a constant 0.088 01 for two interdependent random networks regardless of the average degree. In particular, we find that the proposed method has higher reinforcement efficiency compared to the node-reinforced method, and its superiority in scale-free networks becomes more obvious as the coupling strength increases. Moreover, the heterogeneity of the network structure profoundly affects the reinforcement efficiency. These findings may provide several useful suggestions for designing more resilient interdependent networks.

A Hadamard coin driven quantum walk (i.e., Hadamard walk) model is proposed to identify the important edges of undirected complex networks. In this proposed model, the importance of an edge is scored through the observed probabilities on a pair of nodes with a common edge, based on which the rankings of all important edges are obtained according to the score of each edge. By considering the robustness index of the complex network as estimation standard, experimental results indicate that the capability of the proposed Hadamard walk model to identify important edges is 4.59%∼20.03% higher than existing algorithms in static complex networks. Moreover, to further establish its utility, the proposed model was deployed in a dynamic complex network involving a typical communication scenario found in unmanned aerial vehicle (UAV) swarms. Specifically, we implemented the proposed model in simulations to select significant UAV nodes in a dynamic network and outcomes indicate that our model outperforms various algorithms in the verification of epidemic dynamics model.

Understanding wildlife population structure and connectivity can help managers identify conservation strategies, as structure can facilitate the study of population changes and habitat connectivity can provide information on dispersal and biodiversity. To facilitate the use of wildlife monitoring data for improved adaptive management, we developed a novel approach to define hierarchical tiers (multiple scales) of population structure. We defined population structure by combining graph theory with biological inference about dispersal capability (based on movement, gene flow, and habitat condition) and functional processes affecting movement (e.g. habitat selection across scales of landscape preferences). First, we developed least‐cost paths between high fidelity sites (habitat patches) using a cost surface, informed from functional processes of habitat characteristics to account for resistance of inter‐patch movements. Second, we combined the paths into a multi‐path graph construct. Third, we used information on potential connectivity (dispersal distances) and functional connectivity (permeability of fragmented landscapes based on selection preferences) to decompose the graph into hierarchical tiers of connected subpopulations, denoting the degree that dispersal affected population structure. As a case study, we applied our approach across the greater sage‐grouse (Centrocercus urophasianus) range, a species of conservation concern in western United States. We described the relative importance of local populations and where to potentially avoid landscape disturbances that may negatively affect population connectivity using centrality measures supported by graph theory, and we demonstrated close alignment of the resulting population structure with population densities. This method can be adapted for other species with site fidelity and used as a management tool to evaluate population trends and responses to landscape changes across different temporal and spatial scales.

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion algorithm is Soft-Impute, which exploits the special "sparse plus low-rank" structure of the matrix iterates to allow efficient SVD in each iteration. Though Soft-Impute is a proximal algorithm, it is generally believed that acceleration destroys the special structure and is thus not useful. In this paper, we show that Soft-Impute can indeed be accelerated without comprising this structure. To further reduce the iteration time complexity, we propose an approximate singular value thresholding scheme based on the power method. Theoretical analysis shows that the proposed algorithm still enjoys the fast
$O(1/T^2)$
convergence rate of accelerated proximal algorithms. We further extend the proposed algorithm to tensor completion with the scaled latent nuclear norm regularizer. We show that a similar "sparse plus low-rank" structure also exists, leading to low iteration complexity and fast
$O(1/T^2)$
convergence rate. Extensive experiments demonstrate that the proposed algorithm is much faster than Soft-Impute and other state-of-the-art matrix and tensor completion algorithms.

Scientific Reports 6 : Article number: 27823; 10.1038/srep27823 published online: 14 June 2016 ; updated: 25 August 2016 This Article contains errors in the Acknowledgements section.

Identifying a set of influential spreaders in complex networks plays a crucial role in effective information spreading. A simple strategy is to choose top-$r$ ranked nodes as spreaders according to influence ranking method such as PageRank, ClusterRank and $k$-shell decomposition. Besides, some heuristic methods such as hill-climbing, SPIN, degree discount and independent set based are also proposed. However, these approaches suffer from a possibility that some spreaders are so close together that they overlap sphere of influence or time consuming. In this report, we present a simply yet effectively iterative method named VoteRank to identify a set of decentralized spreaders with the best spreading ability. In this approach, all nodes vote in a spreader in each turn, and the voting ability of neighbors of elected spreader will be decreased in subsequent turn. Experimental results on four real networks show that under Susceptible-Infected-Recovered (SIR) model, VoteRank outperforms the traditional benchmark methods on both spreading speed and final affected scale. What's more, VoteRank is also superior to other group-spreader identifying methods on computational time.

We elaborate on a linear time implementation of the Collective Influence (CI) algorithm introduced by Morone, Makse, Nature 524, 65 (2015) to find the minimal set of influencers in a network via optimal percolation. We show that the computational complexity of CI is O(N log N) when removing nodes one-by-one, with N the number of nodes. This is made possible by using an appropriate data structure to process the CI values, and by the finite radius l of the CI sphere. Furthermore, we introduce a simple extension of CI when l is infinite, the CI propagation (CI_P) algorithm, that considers the global optimization of influence via message passing in the whole network and identifies a slightly smaller fraction of influencers than CI. Remarkably, CI_P is able to reproduce the exact analytical optimal percolation threshold obtained by Bau, Wormald, Random Struct. Alg. 21, 397 (2002) for cubic random regular graphs, leaving little improvement left for random graphs. We also introduce the Collective Immunization Belief Propagation algorithm (CI_BP), a belief-propagation (BP) variant of CI based on optimal immunization, which has the same performance as CI_P. However, this small augmented performance of the order of 1-2 % in the low influencers tail comes at the expense of increasing the computational complexity from O(N log N) to O(N^2 log N), rendering both, CI_P and CI_BP, prohibitive for finding influencers in modern-day big-data. The same nonlinear running time drawback pertains to a recently introduced BP-decimation (BPD) algorithm by Mugisha, Zhou, arXiv:1603.05781. For instance, we show that for big-data social networks of typically 200 million users (eg, active Twitter users sending 500 million tweets per day), CI finds the influencers in less than 3 hours running on a single CPU, while the BP algorithms (CI_P, CI_BP and BDP) would take more than 3,000 years to accomplish the same task.

Recently, the abundance of digital data is enabling the implementation of graph-based ranking algorithms that provide system level analysis for ranking publications and authors. Here, we take advantage of the entire Physical Review publication archive (1893-2006) to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer. On this network, we define a ranking method based on a diffusion algorithm that mimics the spreading of scientific credits on the network. We compare the results obtained with our algorithm with those obtained by local measures such as the citation count and provide a statistical analysis of the assignment of major career awards in the area of physics. A website where the algorithm is made available to perform customized rank analysis can be found at the address http://www.physauthorsrank.org.

The study of network disintegration has attracted much attention due to its wide applications, including suppressing the epidemic spreading, destabilizing terrorist network, preventing financial contagion, controlling the rumor diffusion and perturbing cancer networks. The crux of this matter is to find the critical nodes whose removal will lead to network collapse. This paper studies the disintegration of networks with incomplete link information. An effective method is proposed to find the critical nodes by the assistance of link prediction techniques. Extensive experiments in both synthetic and real networks suggest that, by using link prediction method to recover partial missing links in advance, the method can largely improve the network disintegration performance. Besides, to our surprise, we find that when the size of missing information is relatively small, our method even outperforms than the results based on complete information. We refer to this phenomenon as the “comic effect” of link prediction, which means that the network is reshaped through the addition of some links that identified by link prediction algorithms, and the reshaped network is like an exaggerated but characteristic comic of the original one, where the important parts are emphasized.

Complex networks with inhomogeneous topology are very fragile to intentional attacks on the "hub nodes". It is very important and desirable to evaluate the node importance and find these "hub nodes". The networks agglomeration is defined firstly. A node contraction method of evaluation of node importance in complex networks is proposed based on a new evaluation criterion, i. e. the most important node is the one whose contraction results in the largest increase of the networks agglomeration. With the node contraction method, both degree and position of a node are considered and the disadvantage of node deletion method is avoided. An algorithm whose time complexity is O(n3) is proposed. Final experiments verify its efficiency.

Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator, in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtain a family of H-indices that can be used to measure a node's importance. We also prove that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a node's coreness in large-scale evolving networks. Numerical analyses of the susceptible-infected-removed spreading dynamics on disparate real networks suggest that the H-index is a good tradeoff that in many cases can better quantify node influence than either degree or coreness.

PLAD (plasma doping) is promising for both evolutionary and revolutionary doping options because of its unique advantages which can overcome or minimize many of the issues of the beam-line (BL) based implants. In this talk, I present developments of PLAD on both planar and non-planar 3D device structures. Comparing with the conventional BL implants, PLAD shows not only a significant production enhancement, but also a significant device performance improvement and 3D structure doping capability, including an 80% contact resistance reduction, more than 25% drive current increase on planar devices, and 23% series resistance reduction, 25% drive current increase on non-planar 3D devices.

In complex networks, it is of great theoretical and practical significance to identify a set of critical spreaders which help to control the spreading process. Some classic methods are proposed to identify multiple spreaders. However, they sometimes have limitations for the networks with community structure because many chosen spreaders may be clustered in a community. In this paper, we suggest a novel method to identify multiple spreaders from communities in a balanced way. The network is first divided into a great many super nodes and then k spreaders are selected from these super nodes. Experimental results on real and synthetic networks with community structure show that our method outperforms the classic methods for degree centrality, k-core and ClusterRank in most cases.

Similarity is a fundamental measure in network analyses and machine learning
algorithms, with wide applications ranging from personalized recommendation to
socio-economic dynamics. We argue that an effective similarity measurement
should guarantee the stability even under some information loss. With six
bipartite networks, we investigate the stabilities of fifteen similarity
measurements by comparing the similarity matrixes of two data samples which are
randomly divided from original data sets. Results show that, the fifteen
measurements can be well classified into three clusters according to their
stabilities, and measurements in the same cluster have similar mathematical
definitions. In addition, we develop a top-$n$-stability method for
personalized recommendation, and find that the unstable similarities would
recommend false information to users, and the performance of recommendation
would be largely improved by using stable similarity measurements. This work
provides a novel dimension to analyze and evaluate similarity measurements,
which can further find applications in link prediction, personalized
recommendation, clustering algorithms, community detection and so on.

Background:
Computational approaches aided by computer science have been used to predict essential proteins and are faster than expensive, time-consuming, laborious experimental approaches. However, the performance of such approaches is still poor, making practical applications of computational approaches difficult in some fields. Hence, the development of more suitable and efficient computing methods is necessary for identification of essential proteins.
Method:
In this paper, we propose a new method for predicting essential proteins in a protein interaction network, local interaction density combined with protein complexes (LIDC), based on statistical analyses of essential proteins and protein complexes. First, we introduce a new local topological centrality, local interaction density (LID), of the yeast PPI network; second, we discuss a new integration strategy for multiple bioinformatics. The LIDC method was then developed through a combination of LID and protein complex information based on our new integration strategy. The purpose of LIDC is discovery of important features of essential proteins with their neighbors in real protein complexes, thereby improving the efficiency of identification.
Results:
Experimental results based on three different PPI(protein-protein interaction) networks of Saccharomyces cerevisiae and Escherichia coli showed that LIDC outperformed classical topological centrality measures and some recent combinational methods. Moreover, when predicting MIPS datasets, the better improvement of performance obtained by LIDC is over all nine reference methods (i.e., DC, BC, NC, LID, PeC, CoEWC, WDC, ION, and UC).
Conclusions:
LIDC is more effective for the prediction of essential proteins than other recently developed methods.

Social networks constitute a new platform for information propagation, but
its success is crucially dependent on the choice of spreaders who initiate the
spreading of information. In this paper, we remove edges in a network at random
and the network segments into isolated clusters. The most important nodes in
each cluster then form a group of influential spreaders, such that news
propagating from them would lead to an extensive coverage and minimal
redundancy. The method well utilizes the similarities between the
pre-percolated state and the coverage of information propagation in each social
cluster to obtain a set of distributed and coordinated spreaders. Our tests on
the Facebook networks show that this method outperforms conventional methods
based on centrality. The suggested way of identifying influential spreaders
thus sheds light on a new paradigm of information propagation on social
networks.

Most centralities proposed for identifying influential spreaders on social
networks to either spread a message or to stop an epidemic require the full
topological information of the network on which spreading occurs. In practice,
however, collecting all connections between agents in social networks can be
hardly achieved. As a result, such metrics could be difficult to apply to real
social networks. Consequently, a new approach for identifying influential
people without the explicit network information is demanded in order to provide
an efficient immunization or spreading strategy, in a practical sense. In this
study, we seek a possible way for finding influential spreaders by using the
social mechanisms of how social connections are formed in real networks. We
find that a reliable immunization scheme can be achieved by asking people how
they interact with each other. From these surveys we find that the
probabilistic tendency to connect to a hub has the strongest predictive power
for influential spreaders among tested social mechanisms. Our observation also
suggests that people who connect different communities is more likely to be an
influential spreader when a network has a strong modular structure. Our finding
implies that not only the effect of network location but also the behavior of
individuals is important to design optimal immunization or spreading schemes.

The whole frame of interconnections in complex networks hinges on a specific
set of structural nodes, much smaller than the total size, which, if activated,
would cause the spread of information to the whole network [1]; or, if
immunized, would prevent the diffusion of a large scale epidemic [2,3].
Localizing this optimal, i.e. minimal, set of structural nodes, called
influencers, is one of the most important problems in network science [4,5].
Despite the vast use of heuristic strategies to identify influential spreaders
[6-14], the problem remains unsolved. Here, we map the problem onto optimal
percolation in random networks to identify the minimal set of influencers,
which arises by minimizing the energy of a many-body system, where the form of
the interactions is fixed by the non-backtracking matrix [15] of the network.
Big data analyses reveal that the set of optimal influencers is much smaller
than the one predicted by previous heuristic centralities. Remarkably, a large
number of previously neglected weakly-connected nodes emerges among the optimal
influencers. These are topologically tagged as low-degree nodes surrounded by
hierarchical coronas of hubs, and are uncovered only through the optimal
collective interplay of all the influencers in the network. Eventually, the
present theoretical framework may hold a larger degree of universality, being
applicable to other hard optimization problems exhibiting a continuous
transition from a known phase [16].

Recent study shows that the accuracy of the k-shell method in determining
node coreness in a spreading process is largely impacted due to the existence
of core-like group, which has a large k-shell index but a low spreading
efficiency. Based on analysis of the structure of core-like groups in
real-world networks, we discover that nodes in the core-like group are mutually
densely connected with very few out-leaving links from the group. By defining a
measure of diffusion importance for each edge based on the number of
out-leaving links of its both ends, we are able to identify redundant links in
the spreading process, which have a relatively low diffusion importance but
lead to form the locally densely connected core-like group. After filtering out
the redundant links and applying the k-shell method to the residual network, we
obtain a renewed coreness for each node which is a more accurate index to
indicate its location importance and spreading influence in the original
network. Moreover, we find that the performance of the ranking algorithms based
on the renewed coreness are also greatly enhanced. Our findings help to more
accurately decompose the network core structure and identify influential nodes
in spreading processes.

Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell decomposition are the most influential spreaders. However, through a great deal of numerical simulations, we observe that not in all real networks do nodes in high shells are very influential: in some networks the core nodes are the most influential which we call true core, while in others nodes in high shells, even the innermost core, are not good spreaders which we call core-like group. By analyzing the k-core structure of the networks, we find that the true core of a network links diversely to the shells of the network, while the core-like group links very locally within the group. For nodes in the core-like group, the k-shell index cannot reflect their location importance in the network. We further introduce a measure based on the link diversity of shells to effectively distinguish the true core and core-like group, and identify core-like groups throughout the networks. Our findings help to better understand the structural features of real networks and influential nodes.

With great theoretical and practical significance, locating influential nodes
of complex networks is a promising issues. In this paper, we propose a
dynamics-sensitive (DS) centrality that integrates topological features and
dynamical properties. The DS centrality can be directly applied in locating
influential spreaders. According to the empirical results on four real networks
for both susceptible-infected-recovered (SIR) and susceptible-infected (SI)
spreading models, the DS centrality is much more accurate than degree,
$k$-shell index and eigenvector centrality.

A novel composite adsorbent of Fe loaded biomass char (Fe-BC) was fabricated to treat phosphorus in water. Fe-BC was prepared by a procedure including metal complex anion incorporation and precipitation with the pyrolysis char of corn straw as supporting material. The abundant porous structures of the as-prepared sample can be easily observed from its scanning electron microscopy (SEM) images. Observations by X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) analyses show that inorganic nanoiron oxides deposited in the composite could be amorphous hydrous iron oxide α-FeOOH. Adsorption of phosphate onto the Fe-BC composite and its precursor (BC) from aqueous solutions were investigated and discussed. The equilibrium adsorption data of phosphate was described by Langmuir and Freundlich models, and Langmuir isotherm was found to be better fitted than Freundlich isotherm. The maximum phosphate adsorption capacity for phosphate of Fe-BC was as high as 35.43 mg/g, approximately 2.3 times of BC at 25°C. The adsorption kinetics data were better fitted by pseudo-second-order model and intraparticle diffusion model, indicating that the adsorption process was complex. The Fe-BC composite has been proved as an effective adsorbent of phosphate from aqueous solutions owing to its unique porous structures and the greater Lewis basicity of the α-FeOOH.

Complex networks such as the Internet, WWW, transportation networks, power grids, biological neural networks, and scientific cooperation networks of all kinds provide challenges for future technological development. The first systematic presentation of dynamical evolving networks, with many up-to-date applications and homework projects to enhance study. The authors are all very active and well-known in the rapidly evolving field of complex networks. Complex networks are becoming an increasingly important area of research. Presented in a logical, constructive style, from basic through to complex, examining algorithms, through to construct networks and research challenges of the future.

In this paper, we propose a network performance/efficiency measure for the evaluation of financial networks with intermediation. The measure captures risk, transaction cost, price, transaction flow, revenue, and demand information in the context of the decision-makers' behavior in multitiered financial networks that also allow for electronic transactions. The measure is then utilized to define the importance of a financial network component, that is, a node or a link, or a combination of nodes and links. Numerical examples are provided in which the efficiency of the financial network is computed along with the importance ranking of the nodes and links. The results in this paper can be used to assess which nodes and links in financial networks are the most vulnerable in the sense that their removal will impact the efficiency of the network in the most significant way. Hence, the results in this paper have relevance to national security as well as implications for the insurance industry.

The book that launched the Dempster–Shafer theory of belief functions appeared 40 years ago. This intellectual autobiography looks back on how I came to write the book and how its ideas played out in my later work.

The intuitive background for measures of structural centrality in social networks is reviewed and existing measures are evaluated in terms of their consistency with intuitions and their interpretability.

We implement a novel method to detect systemically important financial institutions in a network. The method consists in a simple model of distress and losses redistribution derived from the interaction of banks' balance-sheets through bilateral exposures. The algorithm goes beyond the traditional default-cascade mechanism, according to which contagion propagates only through banks that actually default. We argue that even in the absence of other defaults, distressed-but-non-defaulting institutions transmit the contagion through channels other than solvency: weakness in their balance sheet reduces the value of their liabilities, thereby negatively affecting their interbank lenders even before a credit event occurs. In this paper, we apply the methodology to a unique dataset covering bilateral exposures among all Italian banks in the period 2008-2012. We find that the systemic impact of individual banks has decreased over time since 2008. The result can be traced back to decreasing volumes in the interbank market and to an intense recapitalization process. We show that the marginal effect of a bank's capital on its contribution to systemic risk in the network is considerably larger when interconnectedness is high (good times): this finding supports the regulatory work on counter-cyclical (macroprudential) capital buffers.

The structure characters of weighted complex networks are analysed. The effect of the edge-weight on estimation of node importance is calculated. A new definition of weighted node importance is proposed, and an improved node contraction method in weighted networks is given based on the evaluation criterion, i.e. the most important node is the one whose contraction results are the largest increase of the weighted networks agglomeration. The time complexity of this algorithm is O(n 3), and the improved evaluation method can help exactly to find some critical nodes in complex networks. Final experiments verify the efficiency and feasibility of the proposed method.

In order to quantitatively calculate the invulnerability of the communication network, taking fully connected network as a reference, an evaluation method based on disjoint paths in topology is proposed to define the index of the invulnerability and the vitality of node and link. Meanwhile, a method for calculating the disjoint paths is proposed. The index of the invulnerability is obtained by calculating the ratio of the disjomt paths of the nodes for both target network and fully connected network. Furthermore, according to the size of the value of the invulnerability index in condition of node or link failure, the importance of node and link is evaluated. The correctness and the time and space complexity of the proposed method are discussed. By giving an example and comparing with the evaluation method based on the shortest paths, it is indicated that the proposed method is more reasonable and is better for reflecting the actual communication network performance.

Online social networks became a remarkable development with wonderful social as well as economic impact within the last decade. Currently the most famous online social network, Facebook, counts more than one billion monthly active users across the globe. Therefore, online social networks attract a great deal of attention among practitioners as well as research communities. Taken together with the huge value of information that online social networks hold, numerous online social networks have been consequently valued at billions of dollars. Hence, a combination of this technical and social phenomenon has evolved worldwide with increasing socioeconomic impact. Online social networks can play important role in viral marketing techniques, due to their power in increasing the functioning of web search, recommendations in various filtering systems, scattering a technology (product) very quickly in the market. In online social networks, among all nodes, it is interesting and important to identify a node which can affect the behaviour of their neighbours; we call such node as Influential node. The main objective of this paper is to provide an overview of various techniques for Influential User identification. The paper also includes some techniques that are based on structural properties of online social networks and those techniques based on content published by the users of social network.

Large-scale websites are predominantly built as a service-oriented architecture. Here, services are specialized for a certain task, run on multiple machines, and communicate with each other to serve a user's request. An anomalous change in a metric of one service can propagate to other services during this communication, resulting in overall degradation of the request. As any such degradation is revenue impacting, maintaining correct functionality is of paramount concern: it is important to find the root cause of any anomaly as quickly as possible. This is challenging because there are numerous metrics or sensors for a given service, and a modern website is usually composed of hundreds of services running on thousands of machines in multiple data centers.
This paper introduces MonitorRank, an algorithm that can reduce the time, domain knowledge, and human effort required to find the root causes of anomalies in such service-oriented architectures. In the event of an anomaly, MonitorRank provides a ranked order list of possible root causes for monitoring teams to investigate. MonitorRank uses the historical and current time-series metrics of each sensor as its input, along with the call graph generated between sensors to build an unsupervised model for ranking. Experiments on real production outage data from LinkedIn, one of the largest online social networks, shows a 26% to 51% improvement in mean average precision in finding root causes compared to baseline and current state-of-the-art methods.