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The Dynamics of a Mobile Phone Network
Abstract
The empirical study of network dynamics has been limited by the lack of longitudinal data. Here we introduce a quantitative indicator of link persistence to explore the correlations between the structure of a mobile phone network and the persistence of its links. We show that persistent links tend to be reciprocal and are more common for people with low degree and high clustering. We study the redundancy of the associations between persistence, degree, clustering and reciprocity and show that reciprocity is the strongest predictor of tie persistence. The method presented can be easily adapted to characterize the dynamics of other networks and can be used to identify the links that are most likely to survive in the future.
... Identifying the different mechanisms by which a tie form or decay is a fundamental and challenging question of individual human behavior, but also it can unravel the processes behind group, community and network dynamics that shape our social fabric and, in turn, how that network evolution impact important processes in our society like cooperation [32], disease spreading [15] or information diffusion [18,24,26]. On the other hand, understanding under what condition a tie is more or less likely to decay may shed light on the circumstances under which an observed interaction can be actually considered a genuine social relationship [14,19] and its present and future potential strength in the different processes happening in social networks. ...
... In particular a special attention has been given to endogenous factors, i.e. those properties that can be extrapolated from the network itself to predict future tie behavior. Intensity of previous interactions, reciprocity, network proximity, triadic closure or the existence of common friends are not only predictors of tie formation [21], but also of its persistence in the future [14,31]. In the context of Granovetter's theory of strength of weak ties, strong ties are those which are more likely to persist, since they are structurally embedded (common friends) are more intense (number of interactions), while bridges between communities are weak and, as Burt found [5], they are more likely to decay in the future. ...
... This is largely due to the lack of quality data: although some online social networks have explicit mechanisms to "unfollow" (Twitter) [20] or 'unfriending" (Facebook) [30] other users, the access to structural or intensity data in those platforms is limited in those platforms. On the other hand, most studies infer tie decay from absence of tie activity in large databases [14,31]. This is a potential problem since, given the large burstiness of human interaction [3,26], large inactivity periods could be mistaken as tie decay events. ...
Social networks are made out of strong and weak ties having very different structural and dynamical properties. But, what features of human interaction build a strong tie? Here we approach this question from an practical way by finding what are the properties of social interactions that make ties more persistent and thus stronger to maintain social interactions in the future. Using a large longitudinal mobile phone database we build a predictive model of tie persistence based on intensity, intimacy, structural and temporal patterns of social interaction. While our results confirm that structural (embeddedness) and intensity (number of calls) are correlated with tie persistence, we find that temporal features of communication events are better and more efficient predictors for tie persistence. Specifically, although communication within ties is always bursty we find that ties that are more bursty than the average are more likely to decay, signaling that tie strength is not only reflected in the intensity or topology of the network, but also on how individuals distribute time or attention across their relationships. We also found that stable relationships have and require a constant rhythm and if communication is halted for more than 8 times the previous communication frequency, most likely the tie will decay. Our results not only are important to understand the strength of social relationships but also to unveil the entanglement between the different temporal scales in networks, from microscopic tie burstiness and rhythm to macroscopic network evolution.
... Smartphones have previously been used to infer 95% of self-reported friendships based on communication and proximity [9]. In addition to this, mobile phones have been used in several studies on human behavior [10,11] including communication dynamics [12], mobility [13], and personality [14,15]. ...
... We find that the probability generally increases as the initiative length grows towards 10. This is in line with previous research [12], which has shown that reciprocity is important to link persistence. For initiative lengths greater than 12, the probability drops back again; possibly because this involves only the most dedicated relations, e.g. ...
Human social interaction is often intermittent. Two acquainted persons can have extended periods without social interaction punctuated by periods of repeated interaction. In this case, the repeated interaction can be characterized by a seed initiative by either of the persons and a number of follow-up interactions. The tendency to initiate social interaction plays an important role in the formation of social networks and is in general not symmetric between persons. In this paper, we study the dynamics of initiative by analysing and modeling a detailed call and text message network sampled from a group of 700 individuals. We show that in an average relationship between two individuals, one part is almost twice as likely to initiate communication compared to the other part. The asymmetry has social consequences and ultimately might lead to the discontinuation of a relationship. We explain the observed asymmetry by a positive feedback mechanism where individuals already taking initiative are more likely to take initiative in the future. In general, people with many initiatives receive attention from a broader spectrum of friends than people with few initiatives. Lastly, we compare the likelihood of taking initiative with the basic personality traits of the five factor model.
... Reciprocity (Newman et al. 2002;Garlaschelli and Loffredo 2004), which quantifies how mutually nodes are linked, has been used widely as a basic statistic of directed graphs, which are a special case of directed hypergraphs where every arc has exactly one source node and one destination node. Reciprocity increase understanding of a graph, especially potential organizing principles of it, and has proved useful for various tasks, including trust prediction (Nguyen et al. 2010), persistence prediction (Hidalgo and Rodríguez-Sickert 2008), anomaly detection (Akoglu et al. 2012), and analysis of the spread of a computer virus through emails (Newman et al. 2002). ...
... Motivated by this intuition, we propose Axiom 5 and Axiom 7, which suggest the bound of hyperarc and hypergraph reciprocity measures, respectively. • Reducibility: Reciprocity in an ordinary directed graph is a well-known statistic that is widely used in various fields of study (Nguyen et al. 2010;Hidalgo and Rodríguez-Sickert 2008;Newman et al. 2002) (see Sect. 1 for details). Since a directed hypergraph is a generalization of an ordinary directed graph, one would expect that a directed hypergraph reciprocity measure should be equivalent to the common directed graph reciprocity when applied to any hypergraph containing only hypercars with head sets and tail sets of size 1 (i.e., directed graph. ...
Group interactions are prevalent in a variety of areas. Many of them, including email exchanges, chemical reactions, and bitcoin transactions, are directional, and thus they are naturally modeled as directed hypergraphs, where each hyperarc consists of the set of source nodes and the set of destination nodes. For directed graphs, which are a special case of directed hypergraphs, reciprocity has played a key role as a fundamental graph statistic in revealing organizing principles of graphs and in solving graph learning tasks. For general directed hypergraphs, however, even no systematic measure of reciprocity has been developed. In this work, we investigate the reciprocity of 11 real-world hypergraphs. To this end, we first introduce eight axioms that any reasonable measure of reciprocity should satisfy. Second, we propose HyperRec, a family of principled measures of hypergraph reciprocity that satisfy all the axioms. Third, we develop FastHyperRec, a fast and exact algorithm for computing the measures. Fourth, using them, we examine 11 real-world hypergraphs and discover patterns that distinguish them from random hypergraphs. Lastly, we propose ReDi, an intuitive generative model for directed hypergraphs exhibiting the patterns.
... For example, researchers analyzed the stability of the community in temporal networks [26][27][28]. Based on the temporal network model, we focus on the basic structure of each link in the network [29], which corresponds to the trade relationship between the two economies in a practical sense. The temporal network setup [30] allows us to explore the evolution of the microstructure properties of the international trade network. ...
... For each directed link e ij (t) in a temporal network G t evolving from t = 1 to t = T, the link stability index, which has been first introduced for mobile communication networks [29], is defined as the occurrence probability of e ij (t) = 1: ...
Fertilizer availability is crucial for global food security, and international fertilizer trade plays a vital role in reallocating fertilizers across multiple economies. However, the stability of international fertilizer trade relationships between economies has not been studied. Using 29 year records of the global fertilizer trade from 1990 to 2018, we construct three temporal networks linked to three primary nutrients (nitrogen N, phosphorus P 2 O 5 , and potash K 2 O). After introducing the link stability indicator to the international fertilizer trade system, which shows a very strong positive correlation with whether the trade will continue in the future, we analyze the factors influencing the stability of the fertilizer trade and provide advice for trading participants to establish highly stable transactions. The supply side has a greater impact on the stability of the fertilizer trade than the demand side. For exporting economies, stable exports need to focus on the counterparty’s real demand rather than its economic situation. For importing economies, intermediaries and producers with good economic conditions are stable trading partners, and trade that is geographically closer is always more stable. The methodology used for link stability analysis in this work can be applied to analyzing other directed temporal networks.
... The massive amount of data that is usually recorded and stored by telephone companies has high scientific value to unveil how humans interact among each other and with the urban infrastructure. Mobile phone records have been instrumental to revisit studies addressing the intensity and shape of social behavior (Onnela et al. 2007;Candia et al. 2008;Hidalgo and Rodriguez-Sickert 2008;González et al. 2008;Iqbal et al. 2014;Lenormand et al. 2014;Louail et al. 2014; Barbosa et al. 2018), and in particular, social interactivity (Kovanen 2009;Reades et al. 2009;Ratti et al. 2010;Palchykov et al. 2014;Schläpfer et al. 2014). The deep prevalence of mobile phones and smart cards allows to generate contextually detailed descriptions of the networks describing social interactions and their dependence on the structural environment in which they are embedded Hidalgo and Rodriguez-Sickert 2008;Steenbruggen et al. 2014). ...
... Mobile phone records have been instrumental to revisit studies addressing the intensity and shape of social behavior (Onnela et al. 2007;Candia et al. 2008;Hidalgo and Rodriguez-Sickert 2008;González et al. 2008;Iqbal et al. 2014;Lenormand et al. 2014;Louail et al. 2014; Barbosa et al. 2018), and in particular, social interactivity (Kovanen 2009;Reades et al. 2009;Ratti et al. 2010;Palchykov et al. 2014;Schläpfer et al. 2014). The deep prevalence of mobile phones and smart cards allows to generate contextually detailed descriptions of the networks describing social interactions and their dependence on the structural environment in which they are embedded Hidalgo and Rodriguez-Sickert 2008;Steenbruggen et al. 2014). ...
Cities have been compared to social reactors constrained by the communication and coordination possibilities offered by an urban environment that has only grown since the advent of the industrial age. We attempt to provide a first description of human interactions in the urban environment using Call Detailed Records (CDR) of the major mobile phone communication network operator in Chile. We build communication networks for 145 Chilean cities to describe and characterize the communication behavior of urban dwellers. We center our analysis in observed indicators of social activity, such as the number of contacts, number of calls and total communication time in each city and evaluate their scaling relationship with the number of mobile phones assigned to each city as an approximation of city size. Interestingly, the values of scaling exponents closely match recent explanations proposed in the literature. The topologies of voice-call networks among cities of increasing sizes are slightly assortative, albeit assortativeness decreases with size. Additionally, they show small average path length relative to their sizes, a typical feature of small-world networks. However, they decrease instead of growing when size is taken into account, unlike other complex networks. Different transitivity indices show mixed results. Average Watts-Strogatz clustering coefficient increases in larger cities much more than expected by pure chance as it has been shown in other social networks. On the other hand, the fact that classic transitivity index decreases seem to exhibit a regime change with a decreasing relation with size and an unexpected growth in larger cities. Both transitivity indices, as a whole, could describe among those who are making new interactions as the city grows. All these results indicate that while tightly knit human communities seem to lose cohesion as they grow, such community properties may progressively disappear among the three to four largest urban centers in Chile where the coordination of complex functions requires each city dweller to reach out to a larger network of people and speak for longer periods of time as compared to smaller cities. Finally, although these results are valid for all networks, there is a division into two regimes when networks reach a critical size of ~10,000 nodes, which raises the possibility of an empirical definition of city for Chile.
... La teoría de las redes se ha utilizado para estudiar una variedad de estructuras matemáticas para modelar las relaciones entre pares de elementos de un determinado grupo, por ejemplo: teléfonos móviles (Hidalgo y Rodríguez-Sickert, 2008), estudiantes (Rizzuto et al., 2009), proyectos universitarios (Urbina et al., 2012) y políticos, intereses económicos (Cárdenas et al., 2014), y producción intelectual de grupos de investigación (Pérez et al., 2015), entre otros. ...
... Para lograr este objetivo, nuestra primera tarea fue ofrecer a los profesores y profesionales de apoyo participantes un análisis de la estructura de las redes sociales entre pares de cada curso. Esta tarea fue guiada por la convicción de que la descripción de las características de la estructura de la red (popularidad, el betweenness y las comunidades, entre otras) permite comprender de mejor manera a los estudiantes como parte de esa red (Hidalgo, 2014), así como acceder a aspectos que no se podrían alcanzar con datos demográficos y socioeconómicos (Hidalgo y Rodríguez-Sickert, 2008). ...
Understanding the dynamic of social relationships between peers in a school can provide guidance for strategic decision-making to improve these relationships. Sociograms-images of a particular moment of these relationships-are a useful tool for description, analysis and reflection. Through interviews with teaching staff and other professionals in the school, the use of sociograms was studied, based on the type of network structure in 12 primary-school courses. Analyzing social connections through the theory of networks reveals information not normally visible, and sociograms are not only useful tools to understand relational dynamics in the school, but also to make strategic programs of systemic actions to improve the school environment and to reflect on teachers’ beliefs about relational dynamics in the classroom.
... The recent rise in large-scale digital tracing from mobile devices enabled, for the first time, the study of large populations at once. These digital data sources offer researchers unprecedented access to huge amounts of information on human interactions and behavior (Lazer et al. [32]), enabling large-scale network analysis using data from online social networks (OSN) or mobile phone communication records (Kumar et al. [27], Onnela et al. [43], Hidalgo and Rodriguez-Sickert [20], Lambiotte et al. [29], Eagle et al. [13]). Early studies uncovered structural properties of global OSNs such as Meta (formerly Facebook) or X (formerly Twitter) (Ugander et al. [54], Myers et al. [40]), as well as more localized ones such as Hyves in the Netherlands (Corten [9]) or iWiW in Hungary (Lengyel et al. [34]). ...
... As seen in the figure, all three networks display heterogeneous distributions of edge lifespans. Such heterogeneity has also been observed in human telecommunication networks [35] and insect proximity networks [36], and suggests that the so-called turnover picture gives a better description of the edge dynamics than the ongoing picture [22]. ...
Opinion dynamics on networks has wide applications to empirical and engineered systems and profound prospects in the general study of complex systems. Many efforts have been devoted to understanding how opinion dynamics is affected by network topology. However, human social interactions are best characterized as temporal networks in which ordering of interactions cannot be ignored. Temporal activity patterns including heterogeneous contact strength and interevent times, turnover edge/node dynamics and daily patterns could have significant effects that would not be captured by static aggregate network representations. In this paper, we study the effects of such temporal patterns on the speed of consensus formation in various models of continuous opinion dynamics using three empirical human face-to-face networks from different real-world settings. We find that static, aggregated networks consistently overestimate the speed of simulated consensus formation while weight heterogeneity associated with frequency of interactions has an inhibitory effect on consensus formation relative to the behavior on unweighted networks. Moreover, the speed of consensus formation is found to be highly sensitive to nodal lifetimes, suggesting that randomization protocols that dramatically alter the distribution of lifetimes cannot be relied upon as reference models. On the other hand, temporal patterns including burstiness of interevent times and the lifetime of edges are found to have insignificant effects on consensus formation.
... degree), and the edge (e.g. weight, triadic embeddedness) matter for decay [8,10,11]. This is primarily due to the fact that the usual data brought to bear to study decay processes in recent work (mostly based on networks constructed from interactions mediated via telecommunication technologies) is very thin on actual node attributes. ...
We study a unique network dataset including periodic surveys and electronic logs of dyadic contacts via smartphones. The participants were a sample of freshmen entering university in the Fall 2011. Their opinions on a variety of political and social issues and lists of activities on campus were regularly recorded at the beginning and end of each semester for the first three years of study. We identify a behavioral network defined by call and text data, and a cognitive network based on friendship nominations in ego-network surveys. Both networks are limited to study participants. Since a wide range of attributes on each node were collected in self-reports, we refer to these networks as attribute-rich networks. We study whether student preferences for certain attributes of friends can predict formation and dissolution of edges in both networks. We introduce a method for computing student preferences for different attributes which we use to predict link formation and dissolution. We then rank these attributes according to their importance for making predictions. We find that personal preferences, in particular political views, and preferences for common activities help predict link formation and dissolution in both the behavioral and cognitive networks.
... Here, we strengthen the link between Jacobs' and Newman's theories by asking whether safer looking neighborhoods are more likely to experience more human activity-and hence, experience more natural surveillance. We explore this connection, by combining computer vision methods, that can be used to measure the physical characteristics of neighbor-hoods [34,44,45,43], with mobile phone data, which has become a common proxy for human activity [8,11,18,20,30], for two Italian cities (Rome and Milan). The combination of computer vision and mobile phone data helps us test whether safer looking neighborhoods are more active, and therefore, if neighborhoods that look physically safer could be experiencing more natural surveillance. ...
Policy makers, urban planners, architects, sociologists, and economists are interested in creating urban areas that are both lively and safe. But are the safety and liveliness of neighborhoods independent characteristics? Or are they just two sides of the same coin? In a world where people avoid unsafe looking places, neighborhoods that look unsafe will be less lively, and will fail to harness the natural surveillance of human activity. But in a world where the preference for safe looking neighborhoods is small, the connection between the perception of safety and liveliness will be either weak or nonexistent. In this paper we explore the connection between the levels of activity and the perception of safety of neighborhoods in two major Italian cities by combining mobile phone data (as a proxy for activity or liveliness) with scores of perceived safety estimated using a Convolutional Neural Network trained on a dataset of Google Street View images scored using a crowdsourced visual perception survey. We find that: (i) safer looking neighborhoods are more active than what is expected from their population density, employee density, and distance to the city centre; and (ii) that the correlation between appearance of safety and activity is positive, strong, and significant, for females and people over 50, but negative for people under 30, suggesting that the behavioral impact of perception depends on the demographic of the population. Finally, we use occlusion techniques to identify the urban features that contribute to the appearance of safety, finding that greenery and street facing windows contribute to a positive appearance of safety (in agreement with Oscar Newman's defensible space theory). These results suggest that urban appearance modulates levels of human activity and, consequently, a neighborhood's rate of natural surveillance.
... For our study we used the large-scale hashed mobile phone dataset from a single mobile service provider in a specific European country [14][15][16] . The dataset covers a seven-month period and includes 1.95 billion calls and 489 million text messages. ...
Social networks have turned out to be of fundamental importance both for our understanding human sociality and for the design of digital communication technology. However, social networks are themselves based on dyadic relationships and we have little understanding of the dynamics of close relationships and how these change over time. Evolutionary theory suggests that, even in monogamous mating systems, the pattern of investment in close relationships should vary across the lifespan when post-weaning investment plays an important role in maximising fitness. Mobile phone data sets provide us with a unique window into the structure of relationships and the way these change across the lifespan. We here use data from a large national mobile phone dataset to demonstrate striking sex differences in the pattern in the gender-bias of preferred relationships that reflect the way the reproductive investment strategies of the two sexes change across the lifespan: these differences mainly reflect women's shifting patterns of investment in reproduction and parental care. These results suggest that human social strategies may have more complex dynamics than we have tended to assume and a life-history perspective may be crucial for understanding them.
... We have access to a set of Call Detail Records (CDR) gathered for billing purposes by Orange mobile phone operator, recording 215 million calls made during 45 days by 20 million anonymized mobile phone users. CDRs collect geographical, temporal and interaction information on mobile phone use and show an enormous potential to empirically investigate human dynamics on a society wide scale [26]. Each time an individual makes a call the mobile phone operator registers the connection between the caller and the callee, the duration of the call and the coordinates of the phone tower communicating with the served phone, allowing to reconstruct the user's time-resolved trajectory. ...
An intriguing open question is whether measurements made on Big Data recording human activities can yield us high-fidelity proxies of socio-economic development and well-being. Can we monitor and predict the socio-economic development of a territory just by observing the behavior of its inhabitants through the lens of Big Data? In this paper, we design a data-driven analytical framework that uses mobility measures and social measures extracted from mobile phone data to estimate indicators for socio-economic development and well-being. We discover that the diversity of mobility, defined in terms of entropy of the individual users' trajectories, exhibits (i) significant correlation with two different socio-economic indicators and (ii) the highest importance in predictive models built to predict the socio-economic indicators. Our analytical framework opens an interesting perspective to study human behavior through the lens of Big Data by means of new statistical indicators that quantify and possibly "nowcast" the well-being and the socio-economic development of a territory.
... In human populations, links between individuals may be long-lasting (persistent), e.g. between an infant child and their caregiver; temporary (transient), e.g. between workplace colleagues; or more short-lived (fleeting), e.g. between strangers coming into close proximity on public transport. In a study using a year's mobile phone data as a proxy for the structure and dynamics of a large social network, researchers found that persistent links tend to be reciprocal and are more common for individuals with low degree and high clustering [15]. Many network-based studies in the past have considered fully static network structures, and hence solely investigate the effects of persistent connections between individuals, see [16] for a review of differing approaches. ...
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a dual-layer static-dynamic multiplex network. The static network layer affords tunable clustering and describes an individual's permanent community structure. The dynamic network layer describes the transient connections an individual makes with members of the wider population by imposing constant edge rewiring. We follow the edge-based compartmental modelling approach to derive equations describing the evolution of a susceptible - infected - recovered (SIR) epidemic spreading through this multiplex network of individuals. We derive the basic reproduction number, measuring the expected number of new infectious cases caused by a single infectious individual in an otherwise susceptible population. We validate model equations by showing convergence to pre-existing edge-based compartmental model equations in limiting cases and by comparison with stochastically simulated epidemics. We explore the effects of altering model parameters and multiplex network attributes on resultant epidemic dynamics. We validate the basic reproduction number by plotting its value against associated final epidemic sizes measured from simulation and predicted by model equations for a number of setups. Further, we explore the effect of varying individual model parameters on the basic reproduction number. We conclude with a discussion of the significance and interpretation of the model and its relation to existing research literature. We highlight intrinsic limitations and potential extensions of the present model and outline future research considerations, both experimental and theoretical.
... The sampled network then contains these K nodes and sampled links, but not those links between selected nodes that have not been sampled. Random edge sampling is commonly used to construct a social graph by using information about contacts-e.g., phone calls are sampled and a graph of callers and receivers is constructed [12]. Snowball sampling. ...
Sampling from large networks represents a fundamental challenge for social network research. In this paper, we explore the sensitivity of different sampling techniques (node sampling, edge sampling, random walk sampling, and snowball sampling) on social networks with attributes. We consider the special case of networks (i) where we have one attribute with two values (e.g., male and female in the case of gender), (ii) where the size of the two groups is unequal (e.g., a male majority and a female minority), and (iii) where nodes with the same or different attribute value attract or repel each other (i.e., homophilic or heterophilic behavior). We evaluate the different sampling techniques with respect to conserving the position of nodes and the visibility of groups in such networks. Experiments are conducted both on synthetic and empirical social networks. Our results provide evidence that different network sampling techniques are highly sensitive with regard to capturing the expected centrality of nodes, and that their accuracy depends on relative group size differences and on the level of homophily that can be observed in the network. We conclude that uninformed sampling from social networks with attributes thus can significantly impair the ability of researchers to draw valid conclusions about the centrality of nodes and the visibility or invisibility of groups in social networks.
... These findings contribute to the understanding of various social phenomena. However, traditional research is mainly based on survey data, which contain a small and less representative population and suffer from high costs and subjective bias [10,11]. The small and subjective data may bring statistical bias or even wrong results. ...
Socioeconomic status (SES) and social relations are two important aspects of human social life. Does socioeconomic status influence social relations? If some relationship exists, it will help us understand various social issues such as economic mobility, social segregation, and disparity in health outcomes. Despite long-term efforts, our knowledge about how SES influences the strength and types of social relations is still limited. In this study, we used a large mobile phone dataset in Beijing, China, to study the relationship between SES and the strength and types of social relations at an urban population level. Specifically, we divided the social relations into three types based on users’ spatiotemporal mobility similarity: (1) family members with high similarity on weekday nights and weekends; (2) coworkers with high similarity on weekdays during the daytime; (3) friends with low similarity all the time. An individual’s SES was represented by the housing price in the home location. The results showed that people of higher SES (living in areas with higher housing prices) tend to interact less with others and allocate more time with friends but less time with family and coworkers than people of lower SES. Besides, people of higher SES split their time more unevenly to different social relationships. These findings shed light on solutions related to SES and inequality. For example, people of low SES could learn to expand their social circles by connecting with people who are different from their daily environment, which may bring upward social mobility and improve their well-being.
... Hidalgo and Rodríguez-Sickert [8] examined the relations between edge persistence and structural features (e.g., coreness and reciprocity) in a mobile phone network. Belth et al. [4] proposed a measure of the persistence of activity snippets (i.e., sequences of reoccurring edge-updates) and showed its usefulness in identifying anomalies. ...
... This work belongs to the second category. Studies in this category have revealed (a) universal temporal patterns, such as densification [26], shrinking diameter [26], and power-laws between principle eigenvalues and edge counts [3]; and (b) domain-specific patterns in hyperlink networks [12], metabolic networks (e.g., biochemical reactions and protein interactions) [11], communication networks (e.g., phone calls and texts) [2,16], and friendship networks [7]. ...
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting the instances of each graphlet (i.e., an induced subgraph isomorphism class) has been successful in characterizing local structures of graphs, with many applications. While graphlets have been extended for temporal graphs, the extensions are designed for examining temporally-local subgraphs composed of edges with close arrival times, instead of long-term changes in local structures. In this paper, as a new lens for temporal graph analysis, we study the evolution of distributions of graphlet instances over time in real-world graphs at three different levels (graphs, nodes, and edges). At the graph level, we first discover that the evolution patterns are significantly different from those in random graphs. Then, we suggest a graphlet transition graph for measuring the similarity of the evolution patterns of graphs, and we find out a surprising similarity between the graphs from the same domain. At the node and edge levels, we demonstrate that the local structures around nodes and edges in their early stage provide a strong signal regarding their future importance. In particular, we significantly improve the predictability of the future importance of nodes and edges using the counts of the roles (a.k.a., orbits) that they take within graphlets.
... Link Decay In many networks, links cannot be removed but are rather considered to become inactive or to decay. Research on predicting decay in mobile phone communication networks (Raeder et al. 2011;Hidalgo and Rodriguez-Sickert 2008) thus assumes that links decay if no communication was exchanged between the actors for a particularly chosen time period. Both works conclude that links are more likely to persist when the connection is reciprocated and when either both actors' degrees are lower or both high. ...
We investigate the structural patterns of the appearance and disappearance of links in dynamic knowledge networks. Human knowledge is nowadays increasingly created and curated online, in a collaborative and highly dynamic fashion. The knowledge thus created is interlinked in nature, and an important open task is to understand its temporal evolution. In this paper, we study the underlying mechanisms of changes in knowledge networks which are of structural nature, i.e., which are a direct result of a knowledge network's structure. Concretely, we ask whether the appearance and disappearance of interconnections between concepts (items of a knowledge base) can be predicted using information about the network formed by these interconnections. In contrast to related work on this problem, we take into account the disappearance of links in our study, to account for the fact that the evolution of collaborative knowledge bases includes a high proportion of removals and reverts. We perform an empirical study on the best-known and largest collaborative knowledge base, Wikipedia, and show that traditional indicators of structural change used in the link analysis literature can be classified into four classes, which we show to indicate growth, decay, stability and instability of links. We finally use these methods to identify the underlying reasons for individual additions and removals of knowledge links.
... Reciprocity [13,23], which quantifies how mutually nodes are linked, has been used widely as a basic statistic of directed graphs, which are a special case of directed hypergraphs where every arc has exactly one source node and one destination node. Reciprocity helps understanding of a graph, especially potential organizing principles of it, and has proved useful for various tasks, including trust prediction [24], persistence prediction [14], anomaly detection [3], and analysis of the spread of a computer virus through emails [23]. ...
Group interactions are prevalent in a variety of areas. Many of them, including email exchanges, chemical reactions, and bitcoin transactions, are directional, and thus they are naturally modeled as directed hypergraphs, where each hyperarc consists of the set of source nodes and the set of destination nodes. For directed graphs, which are a special case of directed hypergraphs, reciprocity has played a key role as a fundamental graph statistic in revealing organizing principles of graphs and in solving graph learning tasks. For general directed hypergraphs, however, even no systematic measure of reciprocity has been developed. In this work, we investigate the reciprocity of 11 real-world hypergraphs. To this end, we first introduce eight axioms that any reasonable measure of reciprocity should satisfy. Second, we propose HyperRec, a principled measure of hypergraph reciprocity that satisfies all the axioms. Third, we develop Ferret, a fast and exact algorithm for computing the measure, whose search space is up to 10^{147}x smaller than that of naive computation. Fourth, using them, we examine 11 real-world hypergraphs and discover patterns that distinguish them from random hypergraphs. Lastly, we propose ReDi, an intuitive generative model for directed hypergraphs exhibiting the patterns.
... Depending on the network type, nodes and edges have various meanings. For instance, in a real-world communication network, a node represents each mobile phone set and an edge connects two nodes when a call is made between the two mobile phone sets [5,6]. ...
We introduce hub centrality and study the relation between hub centrality and the degree of each node in the networks. We discover and verify a universal relation between them in various networks generated by the growth method, but the relation is not applied to real-world networks due to the rich-club phenomenon and the presence of local hubs. Through the study of a targeted attack and overload cascading failure, we prove that hub centrality is a meaningful parameter that gives extra insight beyond degree in real-world networks. Especially, we show that the local hubs occupy key positions in real-world networks with higher probabilities to incur global cascading failure. Therefore, we conclude that networks generated by the growth method, which do not include local hubs, have inevitable limitations to describe real-world networks.
... Persistence of Pairwise Edges. Hidalgo and Rodríguez-Sickert [8] examined the relations between edge persistence and structural features (e.g., coreness and reciprocity) in a mobile phone network. Belth et al. [4] proposed a measure of the persistence of activity snippets (i.e., sequences of reoccurring edge-updates) and showed its usefulness in identifying anomalies. ...
A hypergraph is a generalization of an ordinary graph, and it naturally represents group interactions as hyperedges (i.e., arbitrary-sized subsets of nodes). Such group interactions are ubiquitous in many domains: the sender and receivers of an email, the co-authors of a publication, and the items co-purchased by a customer, to name a few. A higher-order interaction (HOI) in a hypergraph is defined as the co-appearance of a set of nodes in any hyperedge. Our focus is the persistence of HOIs repeated over time, which is naturally interpreted as the strength of group relationships, aiming at answering three questions: (a) How do HOIs in real-world hypergraphs persist over time? (b) What are the key factors governing the persistence? (c) How accurately can we predict the persistence? In order to answer the questions above, we investigate the persistence of HOIs in 13 real-world hypergraphs from 6 domains. First, we define how to measure the persistence of HOIs. Then, we examine global patterns and anomalies in the persistence, revealing a power-law relationship. After that, we study the relations between the persistence and 16 structural features of HOIs, some of which are closely related to the persistence. Lastly, based on the 16 structural features, we assess the predictability of the persistence under various settings and find strong predictors of the persistence. Note that predicting the persistence of HOIs has many potential applications, such as recommending items to be purchased together and predicting missing recipients of emails.
... Our work also builds off a set of past studies that have used mobile phone metadata to study social patterns. These studies have used Call Detail Records (CDR, described in Section 2.1) to study population density [17,19], patterns of migration [10,13,15], friendship formation [20,30], social clustering [6,27], and transportation networks [23,28,29]. Most relevant to our work is the use of CDR to study social and economic dynamics in LMICs, including measuring poverty in Afghanistan [4,11], Guatemala [26], Rwanda [8], and Togo [3]; literacy rates in Senegal [34]; women's empowerment in Uganda [36]; and employment shocks in South Asia [38]. ...
Phone sharing is pervasive in many low- and middle-income countries, affecting how millions of people interact with technology and each other. Yet there is very little quantitative evidence available on the extent or nature of phone sharing in resource-constrained contexts. This paper provides a comprehensive quantitative analysis of phone sharing in Togo, and documents how a large cash transfer program during the COVID-19 pandemic impacted sharing patterns. We analyze mobile phone records from the entire Togolese mobile network to measure the movement of SIM cards between SIM card slots (often on different mobile devices). First, we document the prevalence of sharing in Togo, with 22% of SIMs and 7% of SIM slots shared. Second, using administrative data from a government-run cash transfer program, we find that phone sharing is most common among women, young people, and people in rural areas. Finally, we find that the delivery of cash aid via mobile money significantly increases phone sharing among beneficiaries. We discuss the limitations of measuring phone sharing with mobile network data and the implications of our results for future aid programs delivered via mobile money.
... Traditionally, surveys and travel diaries are used to solve these tasks. While valuable, these data sources are expensive, infrequent, offer low population coverage, lack statistical validity at fine geographical scales, and become available with a lag of one or two years after collection [26,27]. Mobile phone data has emerged as a novel source to capture human mobility [28]. ...
As cities expand, human mobility has become a central focus of urban planning and policy making to make cities more inclusive and sustainable. Initiatives such as the “15-minutes city” have been put in place to shift the attention from monocentric city configurations to polycentric structures, increasing the availability and diversity of local urban amenities. Ultimately they expect to increase local walkability and increase mobility within residential areas. While we know how urban amenities influence human mobility at the city level, little is known about spatial variations in this relationship. Here, we use mobile phone, census, and volunteered geographical data to measure geographic variations in the relationship between origin-destination flows and local urban accessibility in Barcelona. Using a Negative Binomial Geographically Weighted Regression model, we show that, globally, people tend to visit neighborhoods with better access to education and retail. Locally, these and other features change in sign and magnitude through the different neighborhoods of the city in ways that are not explained by administrative boundaries, and that provide deeper insights regarding urban characteristics such as rental prices. In conclusion, our work suggests that the qualities of a 15-minutes city can be measured at scale, delivering actionable insights on the polycentric structure of cities, and how people use and access this structure.
... Traditionally, surveys and travel diaries are used to solve these tasks. While valuable, these data sources are expensive, infrequent, offer low population coverage, lack statistical validity at fine geographical scales, and become available with a lag of one or two years after collection [26,27]. Mobile phone data has emerged as a novel source to capture human mobility [28]. ...
As cities expand, human mobility has become a central focus of urban planning and policy making to make cities more inclusive and sustainable. Initiatives such as the "15-minutes city" have been put in place to shift the attention from monocentric city configurations to polycentric structures, increasing the availability and diversity of local urban amenities. Ultimately they expect to increase local walkability and increase mobility within residential areas. While we know how urban amenities influence human mobility at the city level, little is known about spatial variations in this relationship. Here, we use mobile phone, census, and volunteered geographical data to measure geographic variations in the relationship between origin-destination flows and local urban accessibility in Barcelona. Using a Negative Binomial Geographically Weighted Regression model, we show that, globally, people tend to visit neighborhoods with better access to education and retail. Locally, these and other features change in sign and magnitude through the different neighborhoods of the city in ways that are not explained by administrative boundaries, and that provide deeper insights regarding urban characteristics such as rental prices. In conclusion, our work suggests that the qualities of a 15-minutes city can be measured at scale, delivering actionable insights on the polycentric structure of cities, and how people use and access this structure.
... Many complex networks, such as Online Social Networks, are considered temporal networks [22]. Indeed, relationships appear and disappear due to the temporal evolution of the social relationships [20], or due to the offline/online state of users. Usually, social networks are modelled by using a graph. ...
In the last decades, temporal networks played a key role in modelling, understanding, and analysing the properties of dynamic systems where individuals and events vary in time. Of paramount importance is the representation and the analysis of Social Media, in particular Social Networks and Online Communities, through temporal networks, due to their intrinsic dynamism (social ties, online/offline status, users’ interactions, etc..). The identification of recurrent patterns in Online Communities, and in detail in Online Social Groups, is an important challenge which can reveal information concerning the structure of the social network, but also patterns of interactions, trending topics, and so on. Different works have already investigated the pattern detection in several scenarios by focusing mainly on identifying the occurrences of fixed and well known motifs (mostly, triads) or more flexible subgraphs. In this paper, we present the concept on the Incremental Communication Patterns, which is something in-between motifs, from which they inherit the meaningfulness of the identified structure, and subgraph, from which they inherit the possibility to be extended as needed. We formally define the Incremental Communication Patterns and exploit them to investigate the interaction patterns occurring in a real dataset consisting of 17 Online Social Groups taken from the list of Facebook groups. The results regarding our experimental analysis uncover interesting aspects of interactions patterns occurring in social groups and reveal that Incremental Communication Patterns are able to capture roles of the users within the groups.
... Few related studies have considered truckers as the object of exploration. Hidalgo et al. [5] studied the trajectories of 100,000 anonymous mobile phone users for 6 months and found that human trajectories show significant spatiotemporal patterns. Each individual has a unique travel distance scale independent of time and a significant probability of returning to several frequently visited places. ...
A group of individual truckers can be regarded as a swarm intelligence system without central management. With the development of autonomous driving technology, trucker groups will be replaced by driverless vehicles. At that point, a swarm of truckers will become a swarm robotics system. Therefore, considering the design and control of an efficient swarm robotics system, it is essential to investigate the properties and model the behaviors of a swarm of truckers in advance. In this study, we probe the characteristics of both individual truckers and a swarm of truckers using trajectory data of truckers. First, the trajectory data were map matched based on the geographic scale of cities and administrative regions. Then, the properties of the division of labor, pattern formation, and swarm synchronization were obtained through an analysis of the spatiotemporal distribution of radius of gyration, travel distance, and the number of visited places. Because predicting the next visit locations of individuals of a swarm is a measure for modeling swarm behaviors, the prediction model can be used to predict future swarm robotics (driverless trucks) behaviors. Thus, we apply several machine learning models to predict the next locations of truckers. The results show that there are common characteristics and routines embodied in the behavior of the truckers; the swarm shows consistency and regularity. Moreover, the peak predictability of the entire group reached 94%, indicating that our model can predict the behavior of groups and individuals. Our findings provide basis supporting to the future efficient swarm robotics system.
... There have been extensive studies on macroscopic structural patterns [4,13,35,39], microscopic structural patterns [32,33], and dynamical patterns [15,23,27] in real-world pairwise graphs, and numerous realistic graph generators [8,14,25,27,44] for reproducing the discovered patterns have been proposed. In this section, we focus on hypergraphs and review previous studies on empirical patterns in real-world hypergraphs and realistic hypergraph generators. ...
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in the number of nodes in each hyperedge, which provides the expressiveness of hypergraphs, brings about structural differences between graphs and hypergraphs. Especially, the overlaps of hyperedges lead to complex high-order relations beyond pairwise relations, raising new questions that have not been considered in graphs: How do hyperedges overlap in real-world hypergraphs? Are there any pervasive characteristics? What underlying process can cause such patterns? In this work, we closely investigate thirteen real-world hypergraphs from various domains and share interesting observations of overlaps of hyperedges. To this end, we define principled measures and statistically compare the overlaps of hyperedges in real-world hypergraphs and those in null models. Additionally, based on the observations, we propose HyperLap, a realistic hypergraph generative model. HyperLap is (a) Realistic: it accurately reproduces overlapping patterns of real-world hypergraphs, (b) Automatically Fittable: its parameters can be tuned automatically using HyperLap+ to generate hypergraphs particularly similar to a given target hypergraph, (c) Scalable: it generates and fits a hypergraph with 0.7 billion hyperedges within a few hours.
... spreading patterns of mobile viruses and connection strengths between nodes in a social network). The authors of [123] study the correlation between the structure of a mobile phone network and the persistence of its links, highlighting that persistent links tend to be reciprocal and are more common for nodes with low degree and high clustering. The authors of [124] study the human dynamics from mobile phone records. ...
This paper presents the first comprehensive tutorial on a promising research field located at the frontier of two well-established domains: Neurosciences and wireless communications , motivated by the ongoing efforts to define how the sixth generation of mobile networks (6G) will be. In particular, this tutorial first provides a novel integrative approach that bridges the gap between these two, seemingly disparate fields. Then, we present the state-of-the-art and key challenges of these two topics. In particular, we propose a novel systematization that divides the contributions into two groups, one focused on what neurosciences will offer to 6G in terms of new applications and systems architecture (Neurosciences for Wireless), and the other focused on how wireless communication theory and 6G systems can provide new ways to study the brain (Wireless for Neurosciences). For the first group, we concretely explain how current scientific understanding of the brain would enable new application for 6G within the context of a new type of service that we dub brain-type communications and that has more stringent requirements than human-and machine-type communication. In this regard, we expose the key requirements of brain-type communication services and we discuss how future wireless networks can be equipped to deal with such services. Meanwhile, for the second group, we thoroughly explore modern communication system paradigms, including Internet of Bio-nano Things and chaos-based communications, in addition to highlighting how complex systems tools can help bridging 6G and neuroscience applications. Brain-controlled vehicles are then presented as our case study to demonstrate for both groups the potential created by the convergence of neurosciences and wireless communications in 6G. All in all, this tutorial is expected to provide a largely missing articulation between these two emerging fields while delineating concrete ways to move forward in such an interdisciplinary endeavor.
... spreading patterns of mobile viruses and connection strengths between nodes in a social network). The authors of [123] study the correlation between the structure of a mobile phone network and the persistence of its links, highlighting that persistent links tend to be reciprocal and are more common for nodes with low degree and high clustering. The authors of [124] study the human dynamics from mobile phone records. ...
This paper presents the first comprehensive tutorial on a promising research field located at the frontier of two well-established domains: Neurosciences and wireless communications, motivated by the ongoing efforts to define how the sixth generation of mobile networks (6G) will be. In particular, this tutorial first provides a novel integrative approach that bridges the gap between these two, seemingly disparate fields. Then, we present the state-of-the-art and key challenges of these two topics. In particular, we propose a novel systematization that divides the contributions into two groups, one focused on what neurosciences will offer to 6G in terms of new applications and systems architecture (Neurosciences for Wireless), and the other focused on how wireless communication theory and 6G systems can provide new ways to study the brain (Wireless for Neurosciences). For the first group, we concretely explain how current scientific understanding of the brain would enable new application for 6G within the context of a new type of service that we dub braintype communications and that has more stringent requirements than human- and machine-type communication. In this regard, we expose the key requirements of brain-type communication services and we discuss how future wireless networks can be equipped to deal with such services. Meanwhile, for the second group, we thoroughly explore modern communication system paradigms, including Internet of Bio-nano Things and chaosbased communications, in addition to highlighting how complex systems tools can help bridging 6G and neuroscience applications. Brain-controlled vehicles are then presented as our case study. All in all, this tutorial is expected to provide a largely missing articulation between these two emerging fields while delineating concrete ways to move forward in such an interdisciplinary endeavor.
... The hierarchical pattern from empirical data supported the theoretical framework of the 4C model to rank partnership improvement across focus areas. Cesar and Hidalgo (2008) reported that reciprocal relationships were highly probable to persist in the future. To describe network sustainability, a useful computing syntax was developed in the Statistical Analysis System to sort network links beyond the Co-Existing level and identify reciprocal relations across focus areas (see Table 40). ...
The California Children and Families Act of 1998 led to creation of the Kern County Children and Families Commission (First 5 Kern) to support early childhood service programs in Kern County, the third largest county in California that spread a land area as large as the state of New Jersey. In Fiscal Year 2014-15, First 5 Kern administered more than 0.50 per pack tax on cigarettes or equivalent tobacco products. Following a model of results-based accountability, multilevel evaluation findings are summarized in this report to assess the annual impact of the program funding and provide recommendations for service improvement. Five chapters are included in this report. Chapter 1 highlights features of First 5 Kern support; Chapter 2 provides program-specific findings that impact children ages 0-5 and their families; Chapter 3 describes results of partnership building to strengthen the capacity of service integration; Chapter 4 includes longitudinal results from the Core Data Elements (CDE) survey and Family Stability Rubric (FSR) to describe sustainable accomplishments through ongoing improvements. This report ends with Chapter 5: Conclusions and Future Directions to review past recommendations and introduce new recommendations for next year. Quantitative and qualitative approaches have been taken to describe service outcomes in different communities, including the city of Bakersfield that has surpassed St. Louis in population size. The report includes two appendices: (1) Index of Program Acronyms; and (2) Technical Advisory Committee served in FY 2014-15.
... Hence, the rating indicated high consistency in the strength assessment by the mutual partners. A network is expected to have strong sustainability due to the elimination of misunderstandings on the partnership strength (Cesar & Hidalgo, 2008). ...
Since 1998, early childhood education and support services were funded by 50-cents-per-pack tobacco tax through Proposition 10 funding in California. In November, 2016, another proposal was endorsed by voters to add 9 million of the state funding to support 42 programs in Child Health, Family Functioning, and Child Development across Kern County. This report is grounded on a model of result-based accountability to document outcomes of the local service delivery with less per-capital funding from the state. Despite the seemingly equal fund distribution based on the rate of live birth in each county, Kern County is the third largest county in California by land area, and more spending is needed to fund program outreach across a region as large as the state of New Jersey. To justify the state investment and sustain the service improvement, a five-chapter structure has been incorporated in this report to evaluate the funding impact on child well-being this year: Chapter 1 highlights features of First 5 Kern support at the Commission level; Chapter 2 provides program-specific findings that impact children ages 0-5 and their families; Chapter 3 describes results of partnership collaboration to strengthen the system building for service integration; Chapter 4 includes longitudinal results from the Core Data Elements (CDE) survey and Family Stability Rubric (FSR) to describe sustainable accomplishments through the ongoing service improvements. This report ends with Chapter 5: Conclusions and Future Directions to review past recommendations and introduce new recommendations for next year. Both qualitative and quantitative approaches were taken to address three key questions: (1) How much has been done in local child support; (2) How well did the programs perform this year? (3) Are any children and families better off? The report includes two appendices, 26 figures, 78 tables, and 116 reference items.
... When one program claimed another service provider as a partner, a reciprocal acknowledgement from the collaborator is expected to confirm the networking relations. According to Cesar and Hidalgo (2008), reciprocal relationships were highly probable to persist in the future. Partnerships at the Co-Existing level did not demand outreach efforts and were automatically sustainable. ...
In Fiscal Year 2015-16, the California Children and Families Act has appropriated an average of 10 million of the state funding to support 41 programs in Child Health, Family Functioning, and Child Development across Kern County. Due to reduction of tobacco consumption, this report is grounded on a model of result-based accountability to document outcomes of the local service delivery with less per-capital funding from the state. In the third largest county in California by land area, service providers have to spend more money on program outreach to address the need of nearly 900,000 residents across a region as large as the state of New Jersey. To justify the local spending and sustain the service improvement, a five-chapter structure has been incorporated in this report to evaluate the funding impact on child well-being this year: Chapter 1 highlights features of First 5 Kern support at the Commission level; Chapter 2 provides program-specific findings that impact children ages 0-5 and their families; Chapter 3 describes results of partnership collaboration to strengthen the system building for service integration; Chapter 4 includes longitudinal results from the Core Data Elements (CDE) survey and Family Stability Rubric (FSR) to describe sustainable accomplishments through the ongoing service improvements. This report ends with Chapter 5: Conclusions and Future Directions to review past recommendations and introduce new recommendations for next year. Altogether, qualitative and quantitative data were employed to address three key questions: (1) How much has been done in local child support; (2) How well did the programs perform this year? (3) Are any children and families better off? The report includes two appendices: (1) Index of Program Acronyms; and (2) Composition of Technical Advisory Committee.
... It has been shown that mobile network data can be used to uncover nature of the population such as tourists in specific areas [Girardin et al., 2008] and the interaction between the people in the study area [Campbell et al., 2008]. The structure [Onnela et al., 2007a,b], geography [Lambiotte et al., 2008] and dynamics [Hidalgo and Rodriguez-Sickert, 2008] of such networks have been studied and demonstrated to be useful in predicting their change , Vajakas et al., 2018 over time. This social networks and their spatio-temporal structure can also be used for classification of land use [Pei et al., 2014, Jia et al., 2018, assessment of spatial patterns [Reades et al., 2009, Steenbruggen et al., 2013 and understanding the broader spatial structure of cities [Louail et al., 2014, Arribas-Bel and and regions [Arhipova et al., 2018]. ...
Measuring the distribution and dynamics of the population at granular level both spatially and temporally is crucial for understanding the structure and function of the built environment. In this era of big data, there have been numerous attempts to undertake this using the preponderance of unstructured, passive and incidental digital data which are generated from day-to-day human activities. In attempts to collect, analyse and link these widely available datasets at a massive scale, it is easy to put the privacy of the study subjects at risk. This research looks at one such data source - Wi-Fi probe requests generated by mobile devices - in detail, and processes it into granular, long-term information on number of people on the retail high streets of the United Kingdom (UK). Though this is not the first study to use this data source, the thesis specifically targets and tackles the uncertainties introduced in recent years by the implementation of features designed to protect the privacy of the users of Wi-Fi enabled mobile devices. This research starts with the design and implementation of multiple experiments to examine Wi-Fi probe requests in detail, then later describes the development of a data collection methodology to collect multiple sets of probe requests at locations across London. The thesis also details the uses of these datasets, along with the massive dataset generated by the ‘Smart Street Sensor’ project, to devise novel data cleaning and processing methodologies which result in the generation of a high quality dataset which describes the volume of people on UK retail high streets with a granularity of 5 minute intervals since August 2015 across 1000 locations (approx.) in 115 towns. This thesis also describes the compilation of a bespoke ‘Medium data toolkit’ for processing Wi-Fi probe requests (or indeed any other data with a similar size and complexity). Finally, the thesis demonstrates the value and possible applications of such footfall information through a series of case studies. By successfully avoiding the use of any personally identifiable information, the research undertaken for this thesis also demonstrates that it is feasible to prioritise the privacy of users while still deriving detailed and meaningful insights from the data generated by the users.
... Hidalgo et. al [8] find that reciprocity is the strongest predictor of link persistence. Hopcroft et .al ...
Recent years witness the merge of social networks and user-generated content (UGC) platforms. In these new platforms, users establish links to others not only driven by their social relationships in the physical world but also driven by the contents published by others. During this merging process, social networks gradually integrate both social and content links and become unprecedentedly complicated, with the motivation to exploit both the advantages of social viscosity and content attractiveness to reach the best customer retention situation. However, due to the lack of fine-grained data recording such merging phenomena, the co-driven mechanism of social and content links in churn remains unexplored. How do social and content factors jointly influence customers' churn? What is the best ratio of social and content links for retention? Is there a model to capture this co-driven mechanism in churn phenomena? In this paper, we collect a real-world dataset with more than 5.77 million users and 1.15 billion links, with each link being tagged as a social one or a content one. We find that both social and content links have a significant impact on users' churn and they work jointly as a complicated mixture effect. As a result, we propose a novel survival model, which incorporates both social and content factors, to predict churn probability over time. Our model successfully fits the churn distribution in reality and accurately predicts the churn rate of different subpopulations in the future. By analyzing the modeling parameters, we try to strike a balance between social-driven and content-driven links in a user's social network to reach the lowest churn rate. Our model and findings may have potential implications for the design of future social media.
... Reciprocity in bilateral communication provides an additional indicator of tie strength (1,45,46). We measured reciprocity as ...
The strength of long-range ties
It seems reasonable that we would have the closest, strongest ties with people in our immediate social network and that the ties between networks would be weaker. However, Park et al. discovered strong ties that spanned extreme network (not geographic) distances in 11 culturally diverse population-scale networks on four continents—encompassing 56 million Twitter users and 58 million mobile phone subscribers. Although they are fairly rare, strong ties between networks could be important for the spreading of ideas or disease.
Science , this issue p. 1410
... The penetration rate for mobile phones in 2006 was over 120%, so on average everyone had at least one mobile phone in Spain. The network data from this mobile phone company have been used in many publications showing its face and criterion validity (e.g., Bagrow, Wang, & Barabási, 2011;Ercsey-Ravasz, Lichtenwalter, Chawla, & Toroczkai, 2012;Ghoshal & Barabási, 2011;Hidalgo & Rodriguez-Sickert, 2008;Lichtenwalter, Lussier, & Chawla, 2010;Liu, Slotine, & Barabási, 2011;Onnela, Arbesman, Gonzalez, Barabási, & Christakis, 2011;Raeder, Lizardo, Hachen, & Chawla, 2011;Wang, Lizardo, & Hachen, 2013, Wang, Pedreschi, Song, Giannotti, & Barabási, 2011. ...
Sociological theories suggest that urban life affects human sociability in negative ways. People in urban areas are expected to have fewer and weaker ties than those in rural areas. Rural areas should have proportionally more local ties, whereas urban areas have stronger nonlocal ties. We test these hypotheses using comprehensive large-scale data from a mobile phone company in Spain. We examine urban and rural differences in terms of the average number of ties and the composition and strength of local vs. nonlocal ties of subscribers in 6,124 postal codes. Consistent with urbanism theories, networks in more urban areas are smaller but the effect is weak. What is more pronounced are urban-rural differences in the composition and strength of local and nonlocal ties. There is a tradeoff between strength and number of ties. In urban places where local ties are weaker, there are more such ties, whereas in rural places where local ties are stronger, there are fewer local ties. We discuss the theoretical and practical implications of the results.
The article explores major dimensions of mobile phone behaviors in environmental communication and suggests that the impact of mobile phone use upon environmental communication could be explored from at least five dimensions including information seeking, propagation, interaction, organizing, and data collection behaviors. Association between mobile phone use and environmental communication is explained. Dimensions of mobile phone behaviors are illustrated through published studies of environment communication. Major issues related to the mobile phone use are also reviewed.
Previous chapters have shown how mobile network data can be used to infer travel generation and trip distribution. We continue to explore further in this chapter into how to utilize the mobile network data in making inferences about transport mode choice and its social influence. This chapter focuses on social influence in terms of ego-network effect in commuting mode choice, for which a longitudinal mobile phone data that includes both location and communication records is investigated. Methods for inferring social tie strength and transport mode as well as a framework for analyzing social influence in transport mode choice are discussed. The findings reveal that a person’s strong relationships are more essential in determining whether or not driving is the person’s preferred mode of transportation, whereas weak ties are more relevant in determining whether or not public transportation is the person’s preferred mode of transportation. The data also shows that social ties that are geographically nearby have a greater influence on commuting mode choice than those that are farther away. In the case of public transportation, accessibility distance is also a deciding factor. As the access distance increases, the percentage of people who use public transportation decreases. Furthermore, the social network has been found to influence commute mode choice, with the likelihood of choosing a given mode increasing as the percentage of social ties who choose that mode increases. The content discussed in this chapter reflects the idea, motivation, and thinking process in our original work done by Phithakkitnukoon et al. (EPJ Data Sci. 2017;6(11); Soc Netw Anal Min. 2016;6(1)).
Les interactions sociales sont une composante importante de la condition physique des animaux vivants en groupe.L'analyse des réseaux sciaux, et en particulier des réseaux temporels, fournit des outils puissants pour décrire ces interactions sociales et leur évolution. L'étude des réseaux dans leurs aspects temporelles nécessite la disponibilité de grands volumes de données à haute résolution temporelle.L'utilisation du formalisme et des outils du réseau temporel est cependant encore limitée pour les animaux, car les données sur les interactions animales sont encore largement obtenues à partir de méthodes manuelles traditionnelles.Dans cette thèse, nous avons produit des données à haute fréquence à long terme concernant les interactions sociales animales et nous avons conçu un nouveau model de réseau temporel. Ce travail pourrait aider à l'avenir à comprendre les processus écologiques et évolutifs sous-jacents à la formation et à l'organisation des réseaux sociaux, et à étudier comment les changements dans l'environnement, la composition du groupe ou les relations clés uniques influencent l'ensemble de la structure du réseau.
This article introduces a novel task-independent sampler for attributed networks. The problem is important because while data mining tasks on network content are common, sampling on internet-scale networks is costly. Link-trace samplers such as Snowball sampling, Forest Fire, Random Walk, and Metropolis–Hastings Random Walk are widely used for sampling from networks. The design of these attribute-agnostic samplers focuses on preserving salient properties of network structure, and are not optimized for tasks on node content. This article has three contributions. First, we propose a task-independent, attribute aware link-trace sampler grounded in Information Theory. Our sampler greedily adds to the sample the node with the most informative (i.e., surprising) neighborhood. The sampler tends to rapidly explore the attribute space, maximally reducing the surprise of unseen nodes. Second, we prove that content sampling is an NP-hard problem. A well-known algorithm best approximates the optimization solution within 1 − 1/ e , but requires full access to the entire graph. Third, we show through empirical counterfactual analysis that in many real-world datasets, network structure does not hinder the performance of surprise based link-trace samplers. Experimental results over 18 real-world datasets reveal: surprise-based samplers are sample efficient and outperform the state-of-the-art attribute-agnostic samplers by a wide margin (e.g., 45% performance improvement in clustering tasks).
Intelligent vehicular networks emerge as a promising technology to provide efficient data communication in transportation systems and smart cities. At the same time, the popularization of devices with attached sensors has allowed the obtaining of a large volume of data with spatiotemporal information from different entities. In this sense, we are faced with a large volume of vehicular mobility traces being recorded. Those traces provide unprecedented opportunities to understand the dynamics of vehicular mobility and provide data-driven solutions. In this article, we give an overview of the main publicly available vehicular mobility traces; then, we present the main issues for preprocessing these traces. Also, we present the methods used to characterize and model mobility data. Finally, we review existing proposals that apply the hidden knowledge extracted from the mobility trace for vehicular networks. This article provides a survey on studies that use vehicular mobility traces and provides a guideline for the proposition of data-driven solutions in the domain of vehicular networks. Moreover, we discuss open research problems and give some directions to undertake them.
The authors’ focus is on the general statistical features of the time evolution of communities (also called as modules, clusters or cohesive groups) in large social networks. These structural sub-units can correspond to highly connected circles of friends, families, or professional cliques, which are subject to constant change due to the intense fluctuations in the activity and communication patterns of people. The communities can grow by recruiting new members, or contract by loosing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear. According to our results, the time evolution of social groups containing only a few members and larger communities, e.g., institutions show significant differences.
In this study, we analyze the topology of the global currency market using the Granger causality network and attempt to predict its links by utilizing the real effective exchange rate of 61 countries. In this context, we suggest two new link prediction methods using the eta squared as a weight of link. For the network analysis, we focus on the changes in cross-sectional topology and time-varying properties of the causality network during the sub-prime mortgage crisis, the European debt crisis, and the Chinese stock market turbulence. For the link prediction, we evaluate the prediction performance of the proposed method and those of other benchmarks. Based on the results, we observe significant increments in out-degrees and in-degrees of the originating continents of the global financial crisis. Also, we confirm the best prediction accuracy of the weighted causality method based on the statistical significance of higher area under curve in every aspect.
An increasing number of social media users are becoming used to disseminate activities through geotagged posts. The massive available geotagged posts enable collections of users’ footprints over time and offer effective opportunities for mobility prediction. Using geotagged posts for spatio-temporal prediction of future location, however, is challenging. Previous studies either focus on next-place prediction or rely on dense data sources such as GPS data. Introduced in this article is a novel method for future location prediction of individuals based on geotagged social media data. This method employs the hierarchical density-based clustering algorithm with adaptive parameter selection to identify the regions frequently visited by a social media user. A multi-feature weighted Bayesian model is then developed to forecast users’ spatio-temporal locations by combining multiple factors affecting human mobility patterns. Further, an updating strategy is designed to efficiently adjust, over time, the proposed model to the dynamics in users’ mobility patterns. Based on two real-life datasets, the proposed approach outperforms a state-of-the-art method in prediction accuracy by up to 5.34% and 3.30%. Tests show prediction reliability is high with quality predictions, but low in the identification of erroneous locations.
The performance of routing strategies on complex networks can be characterized by two measurements i.e. the traffic capacity and the average packets travel time. By efficiently synthesizing the degree and the dynamic queue length of nodes, we propose the global hybrid (GH) routing strategy. It can achieve higher traffic capacity as well as shorter average packets travel time compared with the state-of-the-art global dynamic (GD) routing strategy and efficient routing (ER) strategy . Moreover, such superiority can be maintained though the queue length information and the corresponding routing paths are updated periodically. Simulation results show that our GH routing strategy can provide the same traffic capacity as the GD routing strategy does, which is more than twice as high as the ER strategy. At the same time, the average packets travel time of the GH routing strategy is more than 20% smaller than that of the GD routing strategy. It is worth noted that longer updating delay makes our GH routing strategy have a greater decline in the average packets travel time. With the updating delay equals 1 0 0 , the decline can be up to 40%. To illustrate the practicability of our GH routing strategy, we also applied it to a scale-free network based data center network. Simulation results reveal that it is practical, effective and can be used in real scenarios to improve the network performance.
Bringing motivational dynamics back into the mainstream of sociological theory and research requires an examination of how the early theoretical legacy was incorporated in five of the most eclectic approaches in contemporary theorizing on social interaction. The paper analyzes (1) the incorporation of utilitarian and behaviorist theories into exchange theory, (2) the transformation of Mead's social behaviorism into interactionist theory, (3) the evolution of Schutz's phenomenology into ethnomethodological theory, (4) the blending of Freud's psychoanalytic approach with elements of interactionist and phenomenological theory in structuration theory, and (5) the combining of Durkheim's structuralism with ethnomethodology and interactionism in interaction-ritual theory. For each of these five theories, the underlying and largely implicit theory of motivation is schematically modeled. Then, a composite of all the models is constructed in an effort to present a provisional theory of interpersonal motivation.
We analyze 330,000 hours of continuous behavioral data logged by the mobile phones of 94 subjects, and compare these observations with self report relational data. The information from these two data sources is overlapping but distinct, and the accuracy of self report data is considerably affected by such factors as the recency and salience of particular interactions. We present a new method for precise measurements of large-scale human behavior based on contextualized proximity and communication data alone, and identify characteristic behavioral signatures of relationships that allowed us to accurately predict 95% of the reciprocated friendships in the study. Using these behavioral signatures we can predict, in turn, individual-level outcomes such as job satisfaction. In a classic piece of ethnography from the 1940s, William Whyte carefully watched the interactions among Italian immigrants on a street corner in Boston's North End (1). Technology today has made the world like the street corner in the 1940s—it is now possible to make detailed observations on the behavior and interactions of massive numbers of people. These observations come from the increasing number of digital traces left in the wake of our actions and interpersonal communications. These digital traces have the potential to revolutionize the study of collective human behavior. This study examines the potential of a particular device that has become ubiquitous over the last decade—the mobile phone—to collect data about human behavior and interactions, in particular from face to face interactions, over an extended period of time. The field devoted to the study of the system of human interactions—social network analysis—has been constrained in accuracy, breadth, and depth because of its reliance on self report data. Self reports are potentially mediated by confounding factors such as beliefs about what constitutes a relationship, ability to recall interactions, and the willingness of individuals to supply accurate information about their relationships. Whole network studies relying on self report relational data typically involve both limited numbers of people (usually less than 100) and a limited number of time points (usually 1). As a result, social network analysis has generally been limited to examining small, well-bounded populations, involving a small number of snapshots of interaction patterns
We model the consumption life cycle of theater attendance for single movies by taking into account the size of the targeted group and the effect of social interactions. We provide an analytical solution of such model, which we contrast with empirical data from the film industry obtaining good agreement with the diverse types of behaviors empirically found. The model grants a quantitative measure of the valorization of this cul- tural good based on the relative values of the coupling between agents who have watched the movie and those who have not. This represents a measurement of the observed quality of the good that is extracted solely from its dynamics, independently of critics reviews.
Systems as diverse as genetic networks or the world wide web are best
described as networks with complex topology. A common property of many large
networks is that the vertex connectivities follow a scale-free power-law
distribution. This feature is found to be a consequence of the two generic
mechanisms that networks expand continuously by the addition of new vertices,
and new vertices attach preferentially to already well connected sites. A model
based on these two ingredients reproduces the observed stationary scale-free
distributions, indicating that the development of large networks is governed by
robust self-organizing phenomena that go beyond the particulars of the
individual systems.
We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in other social networks. These observations imply that the spreading of e-mail viruses is greatly facilitated in real e-mail networks compared to random architectures.
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.
The rich set of interactions between individuals in society results in complex community structure, capturing highly connected circles of friends, families or professional cliques in a social network. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimization of society as a whole. We have developed an algorithm based on clique percolation that allows us to investigate the time dependence of overlapping communities on a large scale, and thus uncover basic relationships characterizing community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist for longer if they are capable of dynamically altering their membership, suggesting that an ability to change the group composition results in better adaptability. The behaviour of small groups displays the opposite tendency-the condition for stability is that their composition remains unchanged. We also show that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime. These findings offer insight into the fundamental differences between the dynamics of small groups and large institutions.
Electronic databases, from phone to e-mails logs, currently provide detailed records of human communication patterns, offering novel avenues to map and explore the structure of social and communication networks. Here we examine the communication patterns of millions of mobile phone users, allowing us to simultaneously study the local and the global structure of a society-wide communication network. We observe a coupling between interaction strengths and the network's local structure, with the counterintuitive consequence that social networks are robust to the removal of the strong ties but fall apart after a phase transition if the weak ties are removed. We show that this coupling significantly slows the diffusion process, resulting in dynamic trapping of information in communities and find that, when it comes to information diffusion, weak and strong ties are both simultaneously ineffective.
• complex systems
• complex networks
• diffusion and spreading
• phase transition
• social systems
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called preferential attachment. Measurements on four networks, namely the science citation network, Internet, actor collaboration and science coauthorship network indicate that the rate at which nodes acquire links depends on the node's degree, offering direct quantitative support for the presence of preferential attachment. We find that for the first two systems the attachment rate depends linearly on the node degree, while for the latter two the dependence follows a sublinear power law. Comment: 4 pages, 3 Figures, RevTex
This paper explores the impact of communication media and the Internet on connectivity between people. Results from a series of social network studies of media use are used as background for exploration of these impacts. These studies explored the use of all available media among members of an academic research group and among distance learners. Asking about media use as well as about the strength of the tie between communicating pairs revealed that those more strongly tied used more media to communicate than weak ties, and that media use within groups conformed to a unidimensional scale, showing a configuration of different tiers of media use supporting social networks of different ties strengths. These results lead to a number of implications regarding media and Internet connectivity, including: how media use can be added to characteristics of social network ties; how introducing a medium can create latent tie connectivity among group members that provides the technical means for activating weak ties, and also how a change in a medium can disrupt existing weak tie networks; how the tiers of media use also suggest that certain media support different kinds of information flow; and the importance of organization-level decisions about what media to provide and promote. The paper concludes with a discussion of implications for Internet effects.
In this paper, we study the linking patterns and discussion topics of political bloggers. Our aim is to measure the degree of interaction between liberal and conservative blogs, and to uncover any differences in the structure of the two communities. Specifically, we analyze the posts of 40 "A-list" blogs over the period of two months preceding the U.S. Presidential Election of 2004, to study how often they referred to one another and to quantify the overlap in the topics they discussed, both within the liberal and conservative communities, and also across communities. We also study a single day snapshot of over 1,000 political blogs. This snapshot captures blogrolls (the list of links to other blogs frequently found in sidebars), and presents a more static picture of a broader blogosphere. Most significantly, we find differences in the behavior of liberal and conservative blogs, with conservative blogs linking to each other more frequently and in a denser pattern.
The tendency for relationships to weaken and disappear I discuss as decay, and functions describing the rate of decay over time I discuss as decay functions. Three conclusions are supported with 4 years of network Ž . data on a study population of bankers and their colleagues in a financial organization. 1 Factors known from cross-sectional evidence to be associated with strong relationships are associated with slow decay; decay is Ž . slower in relations between colleagues with a strong prior relationship inertia , working in the same corporate Ž . Ž . division homophily , prominent in the social hierarchy of bankers status , or connected indirectly through Ž .Ž. many third parties embedding . 2 Regardless of slower decay in certain relations, decay has a pattern over time similar to the population ecology ''liability of newness'' attributed to selection and learning, with the added complication of networks and people aging simultaneously. Decay is a power function of time in which Ž . Ž the probability of decay decreases with tie age years for which a relationship has existed and node age years . Ž . for which a banker has been in the study population . 3 Embedding stability is responsible for the greater stability of older relationships. The decay-inhibiting effects of age occur where embedding is disrupted but not where embedding is continuous. The third conclusion is interesting in highlighting the first derivative of social structure as a causal variable: embedding has to be measured for its change, rather than level, to see both of its distinct effects on relationship decay. q 2000 Elsevier Science B.V. All rights reserved.
We present statistics for the structure and time evolution of a network constructed from user activity in an Internet community. The vastness and precise time resolution of an Internet community offers unique possibilities to monitor social network formation and dynamics. Time evolution of well-known quantities, such as clustering, mixing (degree–degree correlations), average geodesic length, degree, and reciprocity is studied. In contrast to earlier analyses of scientific collaboration networks, mixing by degree between vertices is found to be disassortative. Furthermore, both the evolutionary trajectories of the average geodesic length and of the clustering coefficients are found to have minima.
The amount of structural embeddedness of a tie between two individuals is defined as the extent of overlap of social relations between those two individuals, and presumably reflects the extent of shared foci of activity that bring these individuals together with the same others. It is suggested that, in comparison with other strengths of ties (e.g. strengths of feelings, and frequencies of interactions), structural embeddedness: (1) is less under individuals' control, and therefore (2) tends to be more stable. Analyses of data on the relationships among male students at one small liberal arts college in November and April of their first year in college support the expectation that structural embeddedness is relatively stable, and tends to have some effect on other strengths of ties as well as the continuity of relationships.
We analyze changes in intimate ties in personal community networks. Our data come from interviews conducted a decade apart with 33 Torontonians. There is much turnover in these networks, with only 27% of intimate ties persisting. Durable ties tend to be with intimates who have provided social support, are in frequent telephone contact, or are kin. There was almost complete turnover in the networks of those respondents who got married during the decade. By contrast, the amount of turnover in networks is not associated with whether the respondents had children, moved to a different home, or started/stopped doing paid work during the decade.
The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it offers one of the most extensive database to date on social networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an 8-year period (1991–98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. Three complementary approaches allow us to obtain a detailed characterization. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. In some limits the model can be solved analytically, predicting a two-regime scaling in agreement with the measurements. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically. The combined numerical and analytical results underline the important role internal links play in determining the observed scaling behavior and network topology. The results and methodologies developed in the context of the co-authorship network could be useful for a systematic study of other complex evolving networks as well, such as the world wide web, Internet, or other social networks.
This study uses data collected on 42 women and 432 members of their social networks across a 10-year period beginning with the women's return to school in midlife. The paper addresses three questions: (1) To what extent did the same individuals continue to be active members of the women's social support networks across the decade; (2) to what extent did educational similarity explain which individuals continued to be active members of the women's networks; and (3) did educational similarity explain patterns of both support and socializing? The analyses revealed that between one-quarter and one-third of the associates named as sources of school/work support, general emotional support or socializing continued to be named 10 years after the first interview. The analyses also demonstrated that associates' educational attainment was important in explaining which individuals continued to serve as sources of support for school/work; however, educational attainment was not important in explaining which associates continued to serve as sources of either general emotional support or socializing.
Using data on 60 intentional communities from the Urban Communes Data Set, we examine factors related to the persistence of ties 12 years later, when nearly all members had left the groups. We find strong evidence of triadic effects—people are more likely to remain in contact with others when they share patterns of contact with third parties. Such triadic effects retain importance even when we use alternative measures of contact, and when we control for individual-, dyadic-, and group-level effects including geographic separation. When we examine friendship as opposed to contact, we find that the triadic effects can be decomposed into some effects pertaining to hierarchy and other effects pertaining to reciprocation, giving us a sense of how networks structure themselves over time.
This article uses data on ‘network instability’ to show how differences across multiple measurements on the membership of personal networks can yield important insights into the nature of these networks. The data come from a sample of 234 recent widows, aged 59–85, who completed seven interviews about their networks over a 1-year period. We use these data to investigate the stability of both overall networks and individual ties, as well as the linkage between the stability of individual ties and the stability of the network's aggregate properties. We find that instability in these networks is best thought of in terms of an underlying ‘core-periphery’ structure, whereby some network members are likely to be named repeatedly (the core), while others are relatively unlikely to appear in any given elicitation of the network (the periphery). We explore the implications of this core-periphery structure for cross-sectional elicitations of personal networks.
Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. Here we measure mixing patterns in a variety of networks and find that social networks are mostly assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortatively mixed network, which we study both analytically and numerically. Within this model we find that networks percolate more easily if they are assortative and that they are also more robust to vertex removal.
We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network properties subject to the constraints imposed by a given set of observations. We give exact solutions of models within this class that incorporate arbitrary degree distributions and arbitrary but independent edge probabilities. We also discuss some more complex examples with correlated edges that can be solved approximately or exactly by adapting various familiar methods, including mean-field theory, perturbation theory, and saddle-point expansions.
Social networks evolve over time, driven by the shared activities and affiliations of their members, by similarity of individuals'
attributes, and by the closure of short network cycles. We analyzed a dynamic social network comprising 43,553 students, faculty,
and staff at a large university, in which interactions between individuals are inferred from time-stamped e-mail headers recorded
over one academic year and are matched with affiliations and attributes. We found that network evolution is dominated by a
combination of effects arising from network topology itself and the organizational structure in which the network is embedded.
In the absence of global perturbations, average network properties appear to approach an equilibrium state, whereas individual
properties are unstable.
An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network topology on the process are characterized introducing a quantity called influence and studying its behavior for scale-free and random networks. We show that for this model degree averaged means are constant in time regardless of the number of states involved. Comment: 11 pages, 3 Figures, article class
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Hidalgo was partly supported by the Kellogg Institute at Notre Dame and acknowledges support from NSF grant ITR DMR-0426737, IIS-0513650 and the James S. McDonnell Foundation 220020084. C. Rodriguez-Sickert acknowledges Sam Bowles and the S.F.I. We thank Nicole Leete for proof reading our manuscript
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Acknowledgments
C.A. Hidalgo was partly supported by the Kellogg Institute at Notre Dame and
acknowledges support from NSF grant ITR DMR-0426737, IIS-0513650 and the James
S. McDonnell Foundation 220020084. C. Rodriguez-Sickert acknowledges Sam Bowles
and the S.F.I. We thank Nicole Leete for proof reading our manuscript. Special
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