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A Set of Measures of Centrality Based on Betweenness
Abstract
A Family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced. These measures define centrality in terms of the degree to which a point falls on the shortest path between others and therefore has a potential for control of communication. They may be used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.
... The aim is to analyze the structure of the systems by assuming the relationship between the single elements of the systems: each element is represented by a node, while the link connects two elements related to each other. The centrality metrics, first introduced by [11], represents the measure for better describing the structure of the network by ranking the importance of the nodes [12], such as degree, closeness [11], eigenvector [13], Katz centrality [14], or PageRank [15]. ...
... The aim is to analyze the structure of the systems by assuming the relationship between the single elements of the systems: each element is represented by a node, while the link connects two elements related to each other. The centrality metrics, first introduced by [11], represents the measure for better describing the structure of the network by ranking the importance of the nodes [12], such as degree, closeness [11], eigenvector [13], Katz centrality [14], or PageRank [15]. ...
... Degree centrality. The degree centrality [11] is defined as the number of links incident upon a node and describes the local connectivity of the network. Considering a network N composed of V vertices and E edges, it can be expressed as: ...
Water Distribution Networks (WDNs) are spatially organized infrastructures, whose hydraulic behavior greatly depends on their connectivity properties, i.e., the topological domain. The Complex Network Theory (CNT) provides a wide range of useful functions and metrics that have been tailored for identifying WDNs behavior, even before using hydraulic models. This work exploits the recent studies on the WDN domain, which couple the CNT metrics of centrality tailored for WDN with the intrinsic relevance of the spatial elements of the networks. The study accounts for various combinations of metrics and intrinsic relevance functions aimed at supporting WDN analysis for operational and management tasks. A Digital Water Service (DWS) is used to enable technicians and water companies to replicate the same domain analysis in the ongoing context of digital transformation in WDN sector.
... To counter this, researchers have also used global centrality measures like Betweenness Centrality, Closeness Centrality, and K-shell Decomposition, among others, to Influence Maximization. Freeman (1977) defined Betweenness for a specific node as the ratio of the shortest path which passes through the node and the total number of possible shortest paths in the network. Okamoto et al. (2008) proposed Closeness for a node as the inverse of the sum of the shortest path to all other nodes, thus determining the average closeness of a node to the rest of the graph. ...
Over the last couple of decades, Social Networks have connected people on the web from across the globe and have become a crucial part of our daily life. These networks have also rapidly grown as platforms for propagating products, ideas, and opinions to target a wider audience. This calls for the need to find influential nodes in a network for a variety of reasons, including the curb of misinformation being spread across the networks, advertising products efficiently, finding prominent protein structures in biological networks, etc. In this paper, we propose Modified Community Diversity (MCD), a novel method for finding influential nodes in a network by exploiting community detection and a modified community diversity approach. We extend the concept of community diversity to a two-hop scenario. This helps us evaluate a node’s possible influence over a network more accurately and also avoids the selection of seed nodes with an overlapping scope of influence. Experimental results verify that MCD outperforms various other state-of-the-art approaches on eight datasets cumulatively across three performance metrics.
... The more edges a node has, the greater its direct influence in the network, and the more important the node is in the network. The calculation formula of the degree centrality of node i is (Freeman, 1977): ...
Platinum is widely considered as a critical mineral. According to the most optimistic scenario, the demand for platinum could increase 240-fold globally by 2050 due to the enormous demand potential for green hydrogen and fuel cell vehicles. By integrating network analysis and evaluation indicators, this study develops a framework to visualize the global platinum upstream supply chain, pinpoint supply-related risk areas, and assess the position of various nations in the supply chain. We conclude that there is a significant risk of disruption to the global platinum upstream supply chain. Following is a summary of the main conclusions: First, the global platinum supply network and primary platinum product trade network are both relatively sparse, with poor network connectivity, and the overall network’s risk-resistance is weak. Second, at the non-geographical production country level, the global platinum mining countries, the countries of the producing companies, and the countries of the shareholders of the producing companies are all highly concentrated. Third, the global platinum supply and demand markets are significantly divided, and South Africa holds a significantly stronger national position in the platinum supply network than any other nation, except for the national level of producing companies’ shareholders. However, the national role of South Africa in the trade network is not as strong as that of consuming countries and transit countries. The study proposes that global platinum consuming countries can reduce supply risks by increasing domestic platinum mine production, building international large-scale integrated mining corporations, and raising global supply share by investing in overseas mines.
... A centralidade por intermediação é a propriedade de um espaço recair no caminho que liga outros dois, e sua hierarquia se dá pela quantidade total de vezes que ele aparece nos caminhos que ligam todos os pares de espaços de um sistema (FREEMAN, 1977). Krafta (1994) A Figura 8 apresenta a classificação por tamanho dos CRFs. ...
Os condomínios residenciais fechados (CRFs) são uma das tipologias habitacionais mais difundidas na contemporaneidade e sua implantação é capaz de gerar impactos na estrutura espacial de cidades e regiões. O objetivo deste artigo é problematizar a localização dos CRFs na escala regional, tendo como estudo empírico a Região Metropolitana de Porto Alegre (RMPA). Pretende-se responder às seguintes questões: que tipo de crescimento da mancha urbanizada os CRFs tem gerado? Como se inserem na centralidade metropolitana? A metodologia utiliza análise espacial e modelagem urbana para analisar a localização de 318 CRFs com área acima de 2,0 hectares. Os dados foram obtidos junto à base da METROPLAN-RS e PMPA e por análise de imagens de satélite. Os resultados produzem um panorama da localização dos CRFs, evidenciando uma tendência de ocupação de áreas periféricas, em descontinuidade ao tecido urbano, porém mantendo proximidade aos eixos de maior centralidade da RMPA.
... The classic metrics and the corresponding ones tailored by [16], for a network N composed by V nodes and E links, are defined as follows: [20] is defined as the number of links incident upon a node and describes the local connectivity of the network. It can be expressed as: ...
Mechanical reliability Water Distribution Networks (WDNs) depends on the Isolation Valve System (IVS). In fact, in the event of accidental disruptions or planned maintenance works, segments of the WDNs need to be temporarily disconnected by closing isolation valves to allow pipes repair. This maneuver it modifies the WDN topology and relevant hydraulic behavior. In this paper a recent approach for IVS reliability based on the Complex Network Theory (CNT) has been applied. It couples the construction of the graph of segments and isolation valves generated by the IVS with the risk of segment interruptions, using several WDN-tailored centrality metrics. The study is demonstrated on a real WDN using a Digital Water Service developed ad hoc for enabling technicians and water utilities in targeting the most critical valves in case of failure and thereby defining a lineup for valves inspections and maintenance.
... Therefore for understating the functionality of the configuration in this large system a set of centrality measures such as closeness centrality (Sabidussi, 1966) and betweenness centrality (Freeman, 1977) were employed to assess the local and global depth and integration of the segments in relation to the overall configuration. This model consisting of almost 700k segments was analysed using DepthmapX 0.5 (Turner, et al., n.d.) and the centrality measures were derived from local radius r400m to global radius. ...
The availability of open-source data, coupled with recent advances in technology has made it easier to create large scale urban and regional models used in the field of environmental studies and specifically space syntax. With the use of open data, large scale regional road-centre line models (Turner, 2005) can now be created and processed to explain the spatial configuration as well as the structure of the built environment. While the study of the socio-economic condition of the built environment correlated with the configuration of the space has been the general use of these models, there has been less focus on multi-layered analysis and metrics across a large model. On another hand, with restrictions on datasets from formal resources, the conventional use of space syntax theories and methods are limited. However, incorporating more advanced methods of quantitative analysis, space syntax can compensate for the lack of available formal dataset in reading and/or predicting environmental phenomena. Given that with the available data sources such as Open Street Map, consistent spatial network models are available, RCL segment models can be trained to predict the socio-economic condition of areas where the formal data is not obtainable. This research puts forward a workflow through which, the spatial network model can be used to train a model that predicts mentioned phenomena. This workflow uses a large segment model of the metropolitan area of Tehran and uses the centrality measures from space syntax analysis to train an unsupervised model which can predict possible missing information. It also assesses the efficacy of the model and shows to what extent the model is to be trusted and what the shortcomings of the model are. It is shown that although the models are very efficient in predicting the required conditions there should be a supervised assessment on the parameters of the algorithms to optimize the outcome.
Identifying the most influential spreaders in complex networks is vital for optimally using the network structure and accelerating information diffusion. In most previous methods, the edges are treated equally and their potential importance is ignored. In this paper, a novel algorithm based on Two-Degree Centrality called TDC is proposed to identify influential spreaders. Firstly, the weight of edge is defined based on the power-law function of degree. Then, the node weight is calculated by the weight of its connected edges. Finally, the spreading influence of node is defined by considering the influence degree of the neighborhoods within 2 steps. In order to evaluate the performance of TDC, the Susceptible-Infected-Recovered (SIR) model is used to simulate the spreading process. Experiment results show that TDC can identify influential spreaders more effectively than the other comparative centrality algorithms.KeywordsComplex networkInfluential spreadersTwo-degree centrality
The cascade capacity of a network is the largest threshold fraction of neighbors that should have made a unanimous decision to result in a complete information cascade. The current approach (based on the intra cluster densities of the bridge nodes of the clusters) used to determine the cascade capacity of a network is independent of the choice of the initial adopters. The authors claim that the above approach gives only a lower bound for the cascade capacity of a network and show that the cascade capacity of a network could be indeed larger if the number and topological positions of the nodes chosen as initial adopters are taken into consideration. In this context, they propose a binary search algorithm that could be used to determine the largest possible cascade capacity of a network for a given set of initial adopters. They run the algorithm on 60 real-world networks of diverse domains and observe the cascade capacity of the networks to increase with the percentage of nodes chosen as initial adopters as well as vary with the choice of the centrality metric used to choose the initial adopters.
Past "relative centrality" measures are appropriate only for those contrived or hypothetical communications networks which involve the linking of separate points into a totally connected network. A methodology is proposed for a more common problem encountered by social scientists, that of determining the relative centrality of points within a current empirical social system containing isolates and separate clusters. Thus the concept "point centrality," as employed in this paper, follows Bavelas' (1950) conceptualization of the problem and applies to the relative position of each point in a network rather than to an overall summary indexing the entire network. An approach to analyzing social networks within empirical social organizations is presented whereby a rank ordering as to the relative centrality of each point (point-centrality) can be approximated for each point in the social unit regardless of whether or not they are all part of a single connected network. A computer algorithm for accomplishing this is also presented.
In a group decision situation, influence and perceived leadership were studied as a function of an individual's position in the communication network of his group. The hypotheses were advanced that, regardless of the network he is in, a group member (a) will be influenced less as his group reaches a decision, and (b) will be perceived as the group leader more often when his position in the communication network is more central On an overall basis, both hypotheses were confirmed The hypothesis concerning influence was tenable only in the case of one kind of network.
Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely
determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks.
One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure.
Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
This paper shows how the concept of an incidence matrix of communications can be used to define the entropy of a finite scheme. The properties of the entropy function are examined and the function is found to be best interpreted as a total expected participation index. Data is presented showing the relationship between structural centrality and the new total expected participation index. In general, as the network becomes more centralized the smaller the value of the participation index and as the network becomes more structurally decentralized the greater the participation index.
This paper examines the concept of centrality with respect to small-group communication experiments. An index of centrality is presented which is based on the incidence matrix of actual communications rather than on the deviation matrix of possible communications, as in the Bavelas Index of Centrality. The index takes the value of zero for the homogeneous all-channel graph and the value of unity for the homogeneous wheel graph. The index can be computed for individuals as well as groups. Three examples are computed.
Increasing interest in the application of graph theory to the behavioral sciences is evidenced by the 1963 publication of the book “Applications of Graph Theory to Group Structure” by Claude Flament. Discussed there is the meaning and limitations of the Bavelas measure of centrality. In this article, the author proposes an improvement of this centrality index for both points and graphs in order to extend its analytical utility.
The relationship between the behavior of small groups and the patterns of communication in which they operate was experimentally explored. 100 male M.I.T. students served as subjects. Results are analyzed in detail and the theoretical implications are discussed. It was found that the communication patterns within which the groups worked affected their behavior. "The major behavioral differences attributable to communication patterns were differences in accuracy, total activity, satisfaction of group members, emergence of a leader, and organization of the group." Positions held in the communication patterns affected behavior but centrality of communication patterns was most clearly correlated with behavioral differences.