Network scholars commonly encounter multiple networks, each of which is possibly governed by distinct generation rules while sharing a node group structure. Although the stochastic blockmodeling—detecting such latent group structures with group-specific connection profiles—has been a major topic of recent research, the focus has been given to the assortative group discovery of a single network. Despite its universality, concepts, and techniques for simultaneous characterization of node traits of multilayer networks, constructed by stacking multiple networks into layers, have been limited. Here, we propose a Bayesian multilayer stochastic blockmodeling framework that uncovers layer-common node traits and factors associated with layer-specific network generating functions. Without assuming a priori layer-specific generation rules, our fully Bayesian treatment allows probabilistic inference of latent traits. We extend the approach to detect changes in block structures embedded in temporal layers of network time series. We demonstrate the method using synthetic multilayer networks with assortative, disassortative, core-periphery, and overlapping community structures. Finally, we apply the method to empirical social network datasets, and find that it detects significant latent traits and structural changepoints. In particular, we uncover endogenous historical regimes associated with distinct constellations of states in United States Senate roll call vote similarity patterns.

Antisocial behavior can be contagious, spreading from individual to individual and rippling through social networks. Moreover, it can spread not only through third-party influence from observation, just like innovations or individual behavior do, but also through direct experience, via “pay-it-forward” retaliation. Here, we distinguish between the effects of observation and victimization for the contagion of antisocial behavior by analyzing large-scale digital trace data. We study the spread of cheating in more than a million matches of an online multiplayer first-person shooter game, in which up to 100 players compete individually or in teams against strangers. We identify event sequences in which a player who observes or is killed by a certain number of cheaters starts cheating and evaluate the extent to which these sequences would appear if we preserve the team and interaction structure but assume alternative gameplay scenarios. The results reveal that social contagion is only likely to exist for those who both observe and experience cheating, suggesting that third-party influence and “pay-it-forward” reciprocity interact positively. In addition, the effect is present only for those who both observe and experience more than once, suggesting that cheating is more likely to spread after repeated or multi-source exposure. Approaching online games as models of social systems, we use the findings to discuss strategies for targeted interventions to stem the spread of cheating and antisocial behavior more generally in online communities, schools, organizations, and sports.

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.

Though declining since the 1990s, adolescent pregnancy remains common in the United States. Social supports appear to improve outcomes for pregnant teens; however, teen pregnancy introduces social obstacles, such as stigma. This study investigates how currently or previously pregnant teens’ friendship networks differ from nonpregnant girls using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health) and multilevel regression models. To mitigate concerns that background differences contribute to both pregnancy risk and social networks, girls who experience a pregnancy prior to one data collection time point are compared girls who experience their first pregnancy after this time point. This group who become pregnant after the time point is presumably more similar to already pregnant teens than those never experiencing teen pregnancy. When compared to these girls who become pregnant in the future, those who have already experienced a teen pregnancy report similar numbers of friends (out-nominations) and perceived social acceptance, but are predicted to have fewer peers reporting them as friends (in-nominations) and fewer reciprocated friendships. This suggests that pregnant teens may face stigmatization, of which they may be unaware. It further highlights a new comparison group to account for selection in studies of adolescent pregnancy.

State preferences play an important role in international politics. Unfortunately, actually observing and measuring these preferences are impossible. In general, scholars have tried to infer preferences using either UN voting or alliance behavior. The two most notable measures of state preferences that have flowed from this research area are ideal points (Bailey et al., 2017) and S-scores (Signorino & Ritter, 1999). The basis of both these models is a spatial weighting scheme that has proven useful but discounts higher-order effects that might be present in relational data structures such as UN voting and alliances. We begin by arguing that both alliances and UN voting are simply examples of the multiple layers upon which states interact with one another. To estimate a measure of state preferences, we utilize a tensor decomposition model that provides a reduced-rank approximation of the main patterns across the layers. Our new measure of preferences plausibly describes important state relations and yields important insights on the relationship between preferences, democracy, and international conflict. Additionally, we show that a model of conflict using this measure of state preferences decisively outperforms models using extant measures when it comes to predicting conflict in an out-of-sample context.

This paper elaborates on two theories of social influence processes to multiplex network structures. First, cohesion influence is based on mutual communication made by different types of relations, and second comparison influence that is built on contrasting types of tie. While a system of bundles with a mutual character constitutes the setting for a multiplex network exposure measure within cohesion, comparison influence is defined algebraically through classes of actors in terms of a weakly balanced semiring structure that considers positive, negative, and also ambivalent types of tie. A case study with these approaches is made on an entrepreneurial community network with formal business relations, informal friendship ties, and perceived competition among the firms, and the methods are validated with the Sampson Monastery data set.

A preference for diversity has been identified as an important predictor of tie formation in certain networks, both social and organizational, that also exhibit a high degree of suppleness–the ability to retain their general form and character under stress (Durkheim, 1893/1997. The division of labor in society; Powell et al., 1996. Administrative Science Quarterly 116–145; Powell et al., 2005. American Journal of Sociology, 110(4), 1132–1205; Koput & Gutek, 2010. Gender stratification in the IT industry: Sex, status and social capital. Edward Elgar Publishing). Extant models of preferential attachment, based on popularity, similarity, and cohesion, meanwhile, produce exceedingly brittle networks (Albert et al., 2000. Nature, 406(6794), 378–382; Callaway et al., 2000. Physical Review Letters, 85(25), 5468–5471; Holme et al., 2002. Physical Review E, 65(2), 026107; Shore et al., 2013 Social Networks, 35(1), 116–123). A model of preferential attachment based on diversity is introduced and simulated, demonstrating that a preference for diversity can create a structure characterized by suppleness. This occurs because a preference for diversity promotes overlapping and redundant weak ties during the early stages of network formation.

Ego networks are thought to be influenced by the opportunities provided to associate with others given by our master statuses (e.g., race or sex), by the preferences individuals possess for interaction given our personality traits (e.g., extroverted or neurotic), and by the capacity to manage interactions on an ongoing basis given our cognitive ability to recall network information. However, prior research has been unable to examine all three classes of predictors concurrently. We rectify this deficiency in the literature by using a novel dataset of nearly 1000 respondents collected using controlled laboratory designs; using this dataset, we can simultaneously examine the impact of master statuses, personality traits, and social cognitive competencies on ego network size, structure (i.e., density), and composition (i.e., diversity). We find that all classes of predictors influence our ego networks, though in different ways, and point to new avenues for research into human sociability.

Recently there has been significant work in the social sciences involving ensembles of social networks, that is, multiple, independent, social networks such as students within schools or employees within organizations. There remains, however, very little methodological work on exploring these types of data structures. We present methods for clustering social networks with observed nodal class labels, based on statistics of walk counts between the nodal classes. We extend this method to consider only non-backtracking walks, and introduce a method for normalizing the counts of long walk sequences using those of shorter ones. We then present a method for clustering networks based on these statistics to explore similarities among networks. We demonstrate the utility of this method on simulated network data, as well as on advice-seeking networks in education.

We present a statistical framework for generating predicted dynamic networks based on the observed evolution of social relationships in a population. The framework includes a novel and flexible procedure to sample dynamic networks given a probability distribution on evolving network properties; it permits the use of a broad class of approaches to model trends, seasonal variability, uncertainty, and changes in population composition. Current methods do not account for the variability in the observed historical networks when predicting the network structure; the proposed method provides a principled approach to incorporate uncertainty in prediction. This advance aids in the designing of network-based interventions, as development of such interventions often requires prediction of the network structure in the presence and absence of the intervention. Two simulation studies are conducted to demonstrate the usefulness of generating predicted networks when designing network-based interventions. The framework is also illustrated by investigating results of potential interventions on bill passage rates using a dynamic network that represents the sponsor/co-sponsor relationships among senators derived from bills introduced in the U.S. Senate from 2003 to 2016.

The study of covert networks is plagued by the fact that individuals conceal their attributes and associations. To address this problem, we develop a technology for eliciting this information from qualitative subject-matter experts to inform statistical social network analysis. We show how the information from the subjective probability distributions can be used as input to Bayesian hierarchical models for network data. In the spirit of “proof of concept,” the results of a test of the technology are reported. Our findings show that human subjects can use the elicitation tool effectively, supplying attribute and edge information to update a network indicative of a covert one.

A fundamental goal of systems biology is to create models that describe relationships between biological components. Networks are an increasingly popular approach to this problem. However, a scientist interested in modeling biological (e.g., gene expression) data as a network is quickly confounded by the fundamental problem: how to construct the network? It is fairly easy to construct a network, but is it the network for the problem being considered? This is an important problem with three fundamental issues: How to weight edges in the network in order to capture actual biological interactions? What is the effect of the type of biological experiment used to collect the data from which the network is constructed? How to prune the weighted edges (or what cut-off to apply)? Differences in the construction of networks could lead to different biological interpretations.

Indeed, we find that there are statistically significant dissimilarities in the functional content and topology between gene co-expression networks constructed using different edge weighting methods, data types, and edge cut-offs. We show that different types of known interactions, such as those found through Affinity Capture-Luminescence or Synthetic Lethality experiments, appear in significantly varying amounts in networks constructed in different ways. Hence, we demonstrate that different biological questions may be answered by the different networks. Consequently, we posit that the approach taken to build a network can be matched to biological questions to get targeted answers. More study is required to understand the implications of different network inference approaches and to draw reliable conclusions from networks used in the field of systems biology.

It is well documented that intergenerational ties play important roles in adults’ well-being. However, most studies focus on the impact of individuals’ own perceptions of their ties without considering whether family members’ assessments of these ties affect well-being. We address this question using data from 296 adult children nested within 95 later-life families in which all offspring were interviewed. Applying a mixed-method within-family approach, we explored whether the effect of perceived maternal favoritism on depressive symptoms was increased when siblings shared ego’s perceptions. Multilevel regression analyses revealed that ego’s own perceptions predicted depressive symptoms, but only among daughters. Siblings’ perceptions that egos were most close to mothers did not affect the well-being of daughters or sons. Qualitative analyses suggested that differential effects of perceived favoritism by gender reflected differences in the meaning sons and daughters associated with being favored children. Favored daughters were more likely than favored sons to report that they were emotional caregivers to their mothers; this pattern was especially strong when siblings reinforced egos’ perceptions of being “best suited” for this role. These findings emphasize the salience of egos’ own perceptions, relative to those of family network members, in shaping role embracement and psychological well-being, especially among women.

Where do new markets come from? I construct a network model in which national markets are nodes and flows of recorded music between them are links and conduct a longitudinal analysis of the global pattern of trade in the period 1976–2010. I hypothesize that new export markets are developed through a process of transitive closure in the network of international trade. When two countries' markets experience the same social influences, it brings them close enough together for new homophilous ties to be formed. The implication is that consumption of foreign products helps, not hurts, home-market producers develop overseas markets, but only in those countries that have a history of consuming the same foreign products that were consumed in the home market. Selling in a market changes what is valued in that market, and new market formation is a consequence of having social influences in common.

Social network data are prone to errors regardless their source. This paper focuses on missing data due to actor non-response in valued networks. If actors refuse to provide information, all values for outgoing ties are missing. Partially observed incoming ties to non-respondents and all other patterns for ties between members of the network can be used to impute missing outgoing ties. Many centrality measures are used to determine the most prominent actors inside the network. Using treatments for actor non-response enables us to estimate better the centrality scores of all actors regarding their popularity or prominence. Simulations using initial known blockmodel structures based on three most frequently occurring macro-network structures: cohesive subgroups, core-periphery models, and hierarchical structures were used to evaluate the relative merits of the treatments for non-response. The results indicate that the amount of non-respondents, the type of underlying macro-structure, and the employed treatment have an impact on centrality scores. Regardless of the underlying network structure, the median of the 3-nearest neighbors based on incoming ties performs the best. The adequacy (or not) of the other non-response treatments is contingent on the network macro-structure.

Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.

Balance theory has advanced with interdisciplinary contributions from social science, physical science, engineering, and mathematics. The common focus of attention is social networks in which every individual has either a positive or negative, cognitive or emotional, appraisal of every other individual. The current frontier of work on balance theory is a hunt for a dynamical model that predicts the temporal evolution of any such appraisal network to a particular structure in the complete set of balanced networks allowed by the theory. Finding such a model has proved to be a difficult problem. In this article, we contribute a parsimonious solution of the problem that explicates the conditions under which a network will evolve either to a set of mutually antagonistic cliques or to an asymmetric structure that allows agreement, cooperation, and compromise among cliques.

Numerous works have been proposed to generate random graphs preserving the same properties as real-life large-scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist, and also, just a few models allow to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law, and we give theoretical lower bounds for its modularity. We compare its characteristics with a real-life co-authorship network and show that our model achieves good performances. We believe that our hypergraph model will be an interesting tool that may be used in many research domains in order to reflect better real-life phenomena.

One of the most challenging problems in biomedicine and genomics is the identification of disease biomarkers. In this study, proteomics data from seven major cancers were used to construct two weighted protein–protein interaction networks, i.e., one for the normal and another for the cancer conditions. We developed rigorous, yet mathematically simple, methodology based on the degeneracy at –1 eigenvalues to identify structural symmetry or motif structures in network. Utilizing eigenvectors corresponding to degenerate eigenvalues in the weighted adjacency matrix, we identified structural symmetry in underlying weighted protein–protein interaction networks constructed using seven cancer data. Functional assessment of proteins forming these structural symmetry exhibited the property of cancer hallmarks. Survival analysis refined further this protein list proposing BMI, MAPK11, DDIT4, CDKN2A, and FYN as putative multicancer biomarkers. The combined framework of networks and spectral graph theory developed here can be applied to identify symmetrical patterns in other disease networks to predict proteins as potential disease biomarkers.

There is a growing consensus that dark networks require special methodological considerations, but little attention has been devoted to determining which data transformation processes are best suited to the study of dark networks. Standard approaches to the transformation of multi-modal data “fold” matrices, by binarizing the network and multiplying it against its transpose. Unfortunately, this process produces exaggerated results when applied to weighted networks, and consequently researchers often disregard information on tie-strength when transforming data. This paper evaluates previous attempts to overcome this limitation and assesses projection methods discovered by biologists and physicists, who have studied the problem of transforming weighted multi-modal networks within the specific context of these disciplines. However, the assumptions underlying these transformation processes limit their applicability to dark networks. This paper, therefore, offers the Median Additive Projection Process (MAPP), an approach to data transformation specifically designed for implementation in weighted, multi-modal dark networks. MAPP accounts for the ambiguity inherent to clandestine subject matter by treating relationship strength in a probabilistic fashion. Because agents' one-mode centrality rankings change significantly when different projection processes are applied to the same two-mode network, MAPP allows researchers to more accurately identify central actors in dark networks.