The paper explores the relationship between personality characteristics, sense of community and the structure of personal networks. We collected personal network data from 100 adults, consisting of the information about their 45 alters and ties among them. In addition to the typically used bivariate correlations to analyze the relationship between individual psychological differences and network structure, we propose first the use of typologies of networks and personality and second modified versions of the triadic census in ego-networks. The results show that different personality types tend to occupy a different kind of networks and that newly introduced triadic measures show a relatively higher association with examined psychological attributes than global network measures. Overall, the Psychological Sense of Community showed higher associations with network measures than Big Five personality traits. The former was positively correlated with measures of closed triads among alters, but also with alters embedded in triads with weak ties. Regarding personality traits, Emotional Stability was positively correlated with strong closed triads and with the overall indicator of density. The elaboration of typologies and the census of triads are shown to be effective strategies for the description of personal networks, as well as for the analysis of individual psychological differences.

Historically, health has played an important role in network research, and vice versa (Valente, 2010). This intersection has contributed to how we understand human health as well as the development of network concepts, theory, and methods. Throughout, dynamics have featured prominently. Even when limited to static methods, the emphasis in each of these fields on providing causal explanations has led researchers to draw upon theories that are dynamic, often explicitly. Here, we elaborate a variety of ways to conceptualize the relationship between health and network dynamics, show how these possibilities are reflected in the existing literature, highlight how the articles within this special issue expand that understanding, and finally, identify paths for future research to push this intersection forward.

Triadic closure has been conceptualized and measured in a variety of ways, most famously the clustering coefficient. Existing extensions to affiliation networks, however, are sensitive to repeat group attendance, which does not reflect common interpersonal interpretations of triadic closure. This paper proposes a measure of triadic closure in affiliation networks designed to control for this factor, which manifests in bipartite models as biclique proliferation. To avoid arbitrariness, the paper introduces a triadic framework for affiliation networks, within which a range of measures can be defined; it then presents a set of basic axioms that suffice to narrow this range to the one measure. An instrumental assessment compares the proposed and two existing measures for reliability, validity, redundancy, and practicality. All three measures then take part in an investigation of three empirical social networks, which illustrates their differences.

Population analyses of functional connectivity have provided a rich understanding of how brain function differs across time, individual, and cognitive task. An important but challenging task in such population analyses is the identification of reliable features that describe the function of the brain, while accounting for individual heterogeneity. Our work is motivated by two particularly important challenges in this area: first, how can one analyze functional connectivity data over populations of individuals, and second, how can one use these analyses to infer group similarities and differences. Motivated by these challenges, we model population connectivity data as a multilayer network and develop the multi-node2vec algorithm, an efficient and scalable embedding method that automatically learns continuous node feature representations from multilayer networks. We use multi-node2vec to analyze resting state fMRI scans over a group of 74 healthy individuals and 60 patients with schizophrenia. We demonstrate how multilayer network embeddings can be used to visualize, cluster, and classify functional regions of the brain for these individuals. We furthermore compare the multilayer network embeddings of the two groups. We identify significant differences between the groups in the default mode network and salience network—findings that are supported by the triple network model theory of cognitive organization. Our findings reveal that multi-node2vec is a powerful and reliable method for analyzing multilayer networks. Data and publicly available code are available at https://github.com/jdwilson4/multi-node2vec.

Multilayer graphs consist of several graphs, called layers, where the vertex set of all layers is the same but each layer has an individual edge set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multilayer graphs, including fundamental problems such as maximum-cardinality matching, finding certain clique relaxations, or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of computational tractability.

We examine a model of network formation in single-layer and multiplex networks in which individuals have positive incentives for social ties, closed triangles, and spillover edges. In particular, we investigate the influence of shocks to the network in which the cost of social ties changes after an initial equilibrium. We highlight the emergence of structural entrenchment: the retention of structural features, such as closed triangles and spillover edges, which are formed under historically different conditions from those currently driving network evolution. This work has broad implications for understanding path dependence in the structure and dynamics of single-layer and multiplex networks.

We investigate the impact of misinformation about the contact structure on the ability to predict disease outbreaks. We base our study on 31 empirical temporal networks and tune the frequencies in errors in the node identities or time stamps of contacts. We find that for both these spreading scenarios, the maximal misprediction of both the outbreak size and time to extinction follows an stretched exponential convergence as a function of the error frequency. We furthermore determine the temporal-network structural factors influencing the parameters of this convergence.

A person’s egonet, the set of others with whom that person is connected, is a personal sample of society which especially influences that person’s experience and perceptions of society. We show that egonets systematically misrepresent the general population because each person is included in as many egonets as that person has “friends.” Previous research has recognized that this unequal weighting in egonets leads many people to find that their friends have more friends than they themselves have. This paper builds upon that research to show that people’s egonets provide them with systematically biased samples of the population more generally. We discuss how this ubiquitous egonet bias may have far reaching implications for people’s experiences and perceptions of frequencies of other people’s ties and traits in ways that may influence their own feelings and behaviors. In particular, these egonet biases may help explain people’s tendencies to disproportionately experience and overestimate the prevalence of certain types of deviance and other social behaviors and consequently be influenced toward them. We illustrate egonet bias with analyses of all friends among 63,731 Facebook users. We call for further empirical investigation of egonet biases and their consequences for individuals and society.

Name generators (NGs) and position generators (PGs) have been used to measure resources embedded in personal relationships, namely social support and social capital, respectively. Comparisons of these measures adopted NGs that only elicit a small number of alters (max. 5). In this paper we explore whether the measurement of social capital with NGs eliciting larger personal networks (say 15 to 20 alters) gives more comparable results to the PG in terms of occupational prestige. To address this issue, we designed a personal network questionnaire that combined a multiple name generator (MNG) and a PG and enquired about alter characteristics and alter-alter ties for the two sets of nominations simultaneously, allowing their integrated analysis. The questionnaire was implemented in the software EgoNet to collect data from social/environmental entrepreneurs in Spain (N = 30) and Mexico (N = 30. The analysis shows that the two approaches capture mostly non-overlapping sets of personal network members, suggesting that the PG measured in this case available, but not accessed social capital. Remarkably the NG led to a higher average prestige for this occupational group than the PG, but also a lower heterogeneity in prestige. The consequences of using one or another approach and their interpretations are discussed.

Community-based physical activity programs, such as the Recreovía, are effective in promoting healthy behaviors in Latin America. To understand Recreovías’ challenges and scalability, we characterized its social network longitudinally while studying its participants’ social cohesion and interactions. First, we constructed the Main network of the program’s Facebook profile in 2013 to determine the main stakeholders and communities of participants. Second, we studied the Temporal network growth of the Facebook profiles of three Recreovía locations from 2008 to 2016. We implemented a Time Windows in Networks algorithm to determine observation periods and a scaling model of cities’ growth to measure social cohesion over time. Our results show physical activity instructors as the main stakeholders (20.84% nodes of the network). As emerging cohesion, we found: (1) incremental growth of Facebook users (43–272 nodes), friendships (55–2565 edges), clustering coefficient (0.19–0.21), and density (0.04–0.07); (2) no preferential attachment behavior; and (3) a social cohesion super-linear growth with 1.73 new friendships per joined user. Our results underscore the physical activity instructors’ influence and the emergent cohesion in innovation periods as a co-benefit of the program. This analysis associates the social and healthy behavior dimensions of a program occurring in natural environments under a systemic approach.

Graph kernels for learning and inference on sparse graphs have been widely studied. However, the problem of designing robust kernel functions that can effectively compare graph neighborhoods in the presence of noisy and complex data remains less explored. Here we propose a novel graph-based kernel method referred to as an edit distance graphlet kernel. The method was designed to add flexibility in capturing similarities between local graph neighborhoods as a means of probabilistically annotating vertices in sparse and labeled graphs. We report experiments on nine real-life data sets from molecular biology and social sciences and provide evidence that the new kernels perform favorably compared to established approaches. However, when both performance accuracy and run time are considered, we suggest that edit distance kernels are best suited for inference on graphs derived from protein structures. Finally, we demonstrate that the new approach facilitates simple and principled ways of integrating domain knowledge into classification and point out that our methodology extends beyond classification; e.g. to applications such as kernel-based clustering of graphs or approximate motif finding. Availability: www.sourceforge.net/projects/graphletkernels/

Understanding how person-to-person contagious processes spread through a population requires accurate information on connections between population members. However, such connectivity data, when collected via interview, is often incomplete due to partial recall, respondent fatigue, or study design, e.g. fixed choice designs (FCD) truncate out-degree by limiting the number of contacts each respondent can report. Research has shown how FCD affects network properties, but its implications for predicted speed and size of spreading processes remain largely unexplored. To study the impact of degree truncation on predictions of spreading process outcomes, we generated collections of synthetic networks containing specific properties (degree distribution, degree-assortativity, clustering), and used empirical social network data from 75 villages in Karnataka, India. We simulated FCD using various truncation thresholds and ran a susceptible-infectious-recovered (SIR) process on each network. We found that spreading processes on truncated networks resulted in slower and smaller epidemics, with a sudden decrease in prediction accuracy at a level of truncation that varied by network type. Our results have implications beyond FCD to truncation due to any limited sampling from a larger network. We conclude that knowledge of network structure is important for understanding the accuracy of predictions of process spread on degree truncated networks.

For sexually transmitted infections like HIV to propagate through a population, there must be a path linking susceptible cases to currently infectious cases. The existence of such paths depends in part on the degree distribution. Here, we use simulation methods to examine how two features of the degree distribution affect network connectivity: Mean degree captures a volume dimension, while the skewness of the upper tail captures a shape dimension. We find a clear interaction between shape and volume: When mean degree is low, connectivity is greater for long-tailed distributions, but at higher mean degree, connectivity is greater in short-tailed distributions. The phase transition to a giant component and giant bicomponent emerges as a positive function of volume, but it rises more sharply and ultimately reaches more people in short-tail distributions than in long-tail distributions. These findings suggest that any interventions should be attuned to how practices affect both the volume and shape of the degree distribution, noting potential unanticipated effects. For example, policies that primarily affect high-volume nodes may not be effective if they simply redistribute volume among lower degree actors, which appears to exacerbate underlying network connectivity.

Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes induces a convex subgraph. We show that convexity is an inherent property of many networks that is not present in a random graph. Most convex are spatial infrastructure networks and social collaboration graphs due to their tree-like or clique-like structure, whereas the food web is the only network studied that is truly non-convex. Core–periphery networks are regionally convex as they can be divided into a non-convex core surrounded by a convex periphery. Random graphs, however, are only locally convex meaning that any connected subgraph of size smaller than the average geodesic distance between the nodes is almost certainly convex. We present different measures of network convexity and discuss its applications in the study of networks.

One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become similar to others they interact with) and selection (the tendency to be affected most by the behavior of others who are already similar). Influence tends to promote homogeneity within a society, while selection frequently causes fragmentation. When both forces act simultaneously, it becomes an interesting question to analyze which societal outcomes should be expected.

To study this issue more formally, we analyze a natural stylized model built upon active lines of work in political opinion formation, cultural diversity, and language evolution. We assume that the population is partitioned into “types” according to some traits (such as language spoken or political affiliation). While all types of people interact with one another, only people with sufficiently similar types can possibly influence one another. The “similarity” is captured by a graph on types in which individuals of the same or adjacent types can influence one another. We achieve an essentially complete characterization of (stable) equilibrium outcomes and prove convergence from all starting states. We also consider generalizations of this model.

The hypothesis that violence—especially gang violence—behaves like a contagious disease has grown in popularity in recent years. Scholars have long observed the tendency for violence to cluster in time and space, but little research has focused on empirically unpacking the mechanisms that make violence contagious. In the context of gang violence, retaliation is the prototypical mechanism to explain why violence begets violence. In this study, we leverage relational event models (REMs)—an underutilized yet particularly well-suited modeling technique to study the dynamics of inter-gang violence. We use REMs to examine gang violence’s tendency to replicate—for which retaliation is but one plausible mechanism—and its tendency to diffuse to other groups. We rely on data on conflicts between gangs in a region of Los Angeles over 3 years. We consider how the characteristics of gangs, their spatial proximity, networks of established rivalries, and the evolving history, directionality, and structure of conflicts predict future inter-gang conflicts. While retaliation is an important mechanism for the replication of violence, established rivalries, and inertia—a gang’s tendency to continue attacking the same group—are more important drivers of future violence. We also find little evidence for an emerging pecking order or status hierarchy between gangs suggested by other scholars. However, we find that gangs are more likely to attack multiple gangs in quick succession. We propose that gang violence is more likely to diffuse to other groups because of the boost of internal group processes an initial attack provides.

The dynamic drivers of interfirm interactions across space have rarely been explored in the context of disaster recovery; therefore, the mechanism through which shocks propagate is unclear. This paper uses stochastic actor-oriented modeling to examine how trade networks among the 500 largest Japanese companies evolved during 2010 and 2011, i.e. before and after the Great East Japan Earthquake to identify sources of vulnerability in the system. In contrast to previous reports on broken supply chains, the network displayed only modest change even in the directly affected areas. Controlling for distance and for firm size, we find that when firms changed their partners, they preferred firms that were popular among other firms, that had partners in common with them and that also bought some products or services from them. These findings concur with a criticism that Japanese firms avoid external actors and exhibit inflexibility in reorganizing their networks in times of need, which contrasts with the non-cliquish network structures observed in high-performing economic sectors. The results also highlight the role of energy firms in disaster resilience. Unlike other large Japanese companies that cluster in major urban centers, energy firms are distributed across Japan. However, despite their peripheral physical locations, energy firms are centrally located in trade networks. Thus, while a disaster in any region may affect some energy firms and lead to large-scale temporary shocks, the entire network is unlikely to be disconnected by any region-specific disaster because of the spatial distribution of the topological network core formed by energy companies.

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes themselves. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representation of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we extend the framework for evaluating graph embeddings that was recently introduced in [15]. Now, the framework assigns two scores, local and global, to each embedding that measure the quality of an evaluated embedding for tasks that require good representation of local and, respectively, global properties of the network. The best embedding, if needed, can be selected in an unsupervised way, or the framework can identify a few embeddings that are worth further investigation. The framework is flexible and scalable and can deal with undirected/directed and weighted/unweighted graphs.