During the last century, networks of several types have been used to model a wide range of physical, biological and social systems. For example, Moreno (1934) studied social networks with multiple types of ties, later called multiplex networks (Verbrugge, 1979; Minor, 1983; Lazega & Pattison, 1999) as well as networks with multiple types of actors. Networks with multiple types of actors and relational ties have often been used together: relevant examples are the extensions of two-mode networks studied by Wasserman & Iacobucci (1991), multi-level networks (Lazega & Snijders, 2016), and heterogeneous information networks (Sun et al., 2012). More recently, researchers in physics and computer science have developed models for different types of interconnected networks known as networks of networks (Buldyrev et al., 2010; D'Agostino & Scala, 2014), multilayer social networks (Magnani & Rossi, 2011), and interconnected networks (Dickison et al., 2012).

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.

For reasons of social influence and social logistics, people in closed networks are expected to experience time compression: The more closed a person's network, the steeper the person's discount function, and the more narrow the expected time horizon within which the person deliberates events and behavior. Consistent with the hypothesis, data on managers at the top of three organizations show network closure associated with a social life compressed into daily contact with colleagues. Further, language in closed networks is predominantly about current activities, ignoring the future. Further still, discount functions employed by executive MBA students show more severe discounting by students in more closed networks. Inattention to the future can be argued to impair achievement, however, I find no evidence across the managers of daily contact diminishing the achievement associated with network advantage. I close with comments on replication and extrapolation to language more generally, within-person variation, and select cognitive patterns (closure bias, end of history, and felt status loss).

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.

GLOBALink, a large online network of tobacco control professionals, was active in the promotion of the World Health Organization's Framework Convention on Tobacco Control treaty, an international treaty aimed at reducing the global burden of tobacco-related death and disease. We examined and compared the roles that different countries served in the GLOBALink community during FCTC negotiation and ratification. Previous studies of FCTC ratification found the process adhered to a diffusion of innovation model (Valente et al., 2015). We followed that work by conducting content analyses of discussion messages posted by GLOBALink members representing different countries. Based on the time when they ratified the FCTC, each country was labeled by one of the four adoption stages of the diffusion model and we investigated the amount of shared word use between the different stages. A goodness-of-fit chi-squared test indicated that content was not shared in an expected manner between stages (χ2 = 11,856.45, N = 51,447, p < 0.001). A deeper look at the specific words shared between countries within and between adoption stages provided insight into how interactions between certain countries might have served to support the ratification process.

Many studies have attempted to determine whether an observed network exhibits a so-called “small-world structure.” Such determinations have often relied on a conceptual definition of small worldliness proposed by Watts and Strogatz in their seminal 1998 paper, but recently several quantitative indices of network small worldliness have emerged. This paper reviews and compares three such indices—the small-world quotient (Q), a small-world metric (ω), and the small-world index(SWI)—in the canonical Watts–Strogatz re-wiring model and in four real-world networks. These analyses suggest that researchers should avoid Q, and identify considerations that should guide the choice between ω and SWI.

Prevailing social network frameworks examine the association between peer ties and behaviors, such as smoking, but the role of social isolates is poorly understood. Some theories predict isolated adolescents are protected from peer influence that increases smoking, while others suggest isolates are more likely to initiate smoking because they lack the social control provided by peer friendships. Building on a growing literature that seeks to explain these contradictions by moving beyond a homogeneous understanding of isolation, we identify the relationship between smoking and three distinct dimensions of isolation: avoided (adolescents who do not receive ties), withdrawn (adolescents who do not send ties), and externally oriented (adolescents who claim close out-of-grade friends). We examine the co-evolutionary effects of these dimensions and cigarette smoking using an autoregressive latent trajectory model with PROSPER Peers, a unique, longitudinal network dataset. These data include students (47% male and 86% white) from rural Iowa and Pennsylvania, ranging successively from grades 6–12 in eight waves of data. We find avoided isolation is associated with decreased subsequent smoking in high school. Smoking increases subsequent avoided and withdrawn isolation, but decreases external orientation.

The analysis of multilayer networks is among the most active areas of network science, and there are several methods to detect dense “communities” of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to different types of edges) and show that they have very different bottlenecks, which correspond to rather different notions of what it means for a set of nodes to be a good community. This has direct implications for the behavior of community-detection methods that are based on these random walks.

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.

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.

Social ties are strongly related to well-being. But what characterizes this relationship? This study investigates social mechanisms explaining how social ties affect well-being through social integration and social influence, and how well-being affects social ties through social selection. We hypothesize that highly integrated individuals–those with more extensive and dense friendship networks–report higher emotional well-being than others. Moreover, emotional well-being should be influenced by the well-being of close friends. Finally, well-being should affect friendship selection when individuals prefer others with higher levels of well-being, and others whose well-being is similar to theirs. We test our hypotheses using longitudinal social network and well-being data of 117 individuals living in a graduate housing community. The application of a novel extension of Stochastic Actor-Oriented Models for ordered networks (ordered SAOMs) allows us to detail and test our hypotheses for weak- and strong-tied friendship networks simultaneously. Results do not support our social integration and social influence hypotheses but provide evidence for selection: individuals with higher emotional well-being tend to have more strong-tied friends, and there are homophily processes regarding emotional well-being in strong-tied networks. Our study highlights the two-directional relationship between social ties and well-being, and demonstrates the importance of considering different tie strengths for various social processes.

We consider the task of simultaneous clustering of the two node sets involved in a bipartite network. The approach we adopt is based on use of the exact integrated complete likelihood for the latent blockmodel. Using this allows one to infer the number of clusters as well as cluster memberships using a greedy search. This gives a model-based clustering of the node sets. Experiments on simulated bipartite network data show that the greedy search approach is vastly more scalable than competing Markov chain Monte Carlo-based methods. Application to a number of real observed bipartite networks demonstrate the algorithms discussed.

Chemotherapy is often administered in openly designed hospital wards, where the possibility of patient–patient social influence on health exists. Previous research found that social relationships influence cancer patient's health; however, we have yet to understand social influence among patients receiving chemotherapy in the hospital. We investigate the influence of co-presence in a chemotherapy ward. We use data on 4,691 cancer patients undergoing chemotherapy in Oxfordshire, United Kingdom who average 59.8 years of age, and 44% are Male. We construct a network of patients where edges exist when patients are co-present in the ward, weighted by both patients' time in the ward. Social influence is based on total weighted co-presence with focal patients' immediate neighbors, considering neighbors' 5-year mortality. Generalized estimating equations evaluated the effect of neighbors' 5-year mortality on focal patient's 5-year mortality. Each 1,000-unit increase in weighted co-presence with a patient who dies within 5 years increases a patient's mortality odds by 42% (β = 0.357, CI:0.204,0.510). Each 1,000-unit increase in co-presence with a patient surviving 5 years reduces a patient's odds of dying by 30% (β =−0.344, CI:−0.538,0.149). Our results suggest that social influence occurs in chemotherapy wards, and thus may need to be considered in chemotherapy delivery.

The latent position cluster model is a popular model for the statistical analysis of network data. This model assumes that there is an underlying latent space in which the actors follow a finite mixture distribution. Moreover, actors which are close in this latent space are more likely to be tied by an edge. This is an appealing approach since it allows the model to cluster actors which consequently provides the practitioner with useful qualitative information. However, exploring the uncertainty in the number of underlying latent components in the mixture distribution is a complex task. The current state-of-the-art is to use an approximate form of BIC for this purpose, where an approximation of the log-likelihood is used instead of the true log-likelihood which is unavailable. The main contribution of this paper is to show that through the use of conjugate prior distributions, it is possible to analytically integrate out almost all of the model parameters, leaving a posterior distribution which depends on the allocation vector of the mixture model. This enables posterior inference over the number of components in the latent mixture distribution without using trans-dimensional MCMC algorithms such as reversible jump MCMC. Our approach is compared with the state-of-the-art latentnet (Krivitsky & Handcock, 2015) and VBLPCM (Salter-Townshend & Murphy, 2013) packages.

The position people occupy in their social and professional networks is related to their social status and has strong effects on their access to social resources. While attainment of particular positions is driven by behavioral traits, many biological factors predispose individuals to certain behaviors and motivations. Prior work on exposure to fetal androgens (measured by second-to-fourth digit ratio, 2D:4D) shows that it correlates with behaviors and traits related to social status, which might make people more socially integrated. However, it also predicts certain anti-social behaviors and disorders associated with lower socialization. We explore whether 2D:4D correlates with network position later in life and find that individuals with low 2D:4D become more central in their social environment. Interestingly, low 2D:4D males are more likely to exhibit high betweenness centrality (they connect separated parts of the social structure), while low 2D:4D females are more likely to exhibit high in-degree centrality (more people name them as friends). These gender-specific differences are reinforced by transitivity (the likelihood that one's friends are also friends with one another): neighbors of low 2D:4D men tend not to know each other; the contrary is observed for low 2D:4D women. Our results suggest that biological predispositions influence the organization of human societies and that exposure to prenatal androgens influences different status seeking behaviors in men and women.

In this paper, we seek to advance an updated concept of social space that integrates the multilayer and dynamic statistical network methods currently at the disposal of social network researchers. We demonstrate the analytic value of the new concept of social space that we propose with the help of an illustrative analysis of an organizational field involving organizations' external and internal decisions that congeal into a multilevel system of action that shapes the space of possibilities for other participants in the field. Through these internal and external decisions, organizations seek certain positions in their social space while simultaneously modifying that social space over time. We conclude by arguing that network researchers' choices of goodness-of-fit statistics should reflect a consideration about the dimensions of social space of most interest to the nodes involved.

Despite the growing potential for multiplexity in our complex social world, social network methodology often does not adequately capture this phenomenon. Most commonly in research on egocentric social networks, when respondent designate a tie as both family member and friend, the tendency is to default to “family” prior to aggregation for analysis, potentially ignoring important and meaningful variation. As a result, relatively little is known about multiplexity in personal social networks, and particularly about individuals who are simultaneously kin and friends. To address this gap, we assess the rate of occurrence of kinship/friendship multiplexity, and examine characteristics of alters nominated as friends and kin in comparison to those with unidimensional functionality. We find that this kind of multiplexity is fairly common–comprising about one-fifth of kinship ties and one-fourth of friendship ties. Moreover, cross–listed alters are significantly different from those characterized in one function, serving in greater capacity in terms of provision of support, frequency of contact, closeness, and as resources for discussion of important matters. Our findings underscore the critical need to appropriately classify multiplex kinship/friendship ties to avoid making incorrect inferences about support processes and their effects on outcomes across different relationship types.

Many hierarchically modular systems are structured in a way that resembles an hourglass. This “hourglass effect” means that the system generates many outputs from many inputs through a relatively small number of intermediate modules that are critical for the operation of the entire system, referred to as the waist of the hourglass. We investigate the hourglass effect in general, not necessarily layered, hierarchical dependency networks. Our analysis focuses on the number of source-to-target dependency paths that traverse each vertex, and it identifies the core of a dependency network as the smallest set of vertices that collectively cover almost all dependency paths. We then examine if a given network exhibits the hourglass property or not, comparing its core size with a “flat” (i.e., non-hierarchical) network that preserves the source dependencies of each target in the original network. As a possible explanation for the hourglass effect, we propose the Reuse Preference model that captures the bias of new modules to reuse intermediate modules of similar complexity instead of connecting directly to sources or low complexity modules. We have applied the proposed framework in a diverse set of dependency networks from technological, natural, and information systems, showing that all these networks exhibit the general hourglass property but to a varying degree and with different waist characteristics.

Most people simultaneously belong to several distinct social networks, in which their relations can be different. They have opinions about certain topics, which they share and spread on these networks, and are influenced by the opinions of other persons. In this paper, we build upon this observation to propose a new nodal centrality measure for multiplex networks. Our measure, called Opinion centrality, is based on a stochastic model representing opinion propagation dynamics in such a network. We formulate an optimization problem consisting in maximizing the opinion of the whole network when controlling an external influence able to affect each node individually. We find a mathematical closed form of this problem, and use its solution to derive our centrality measure. According to the opinion centrality, the more a node is worth investing external influence, and the more it is central. We perform an empirical study of the proposed centrality over a toy network, as well as a collection of real-world networks. Our measure is generally negatively correlated with existing multiplex centrality measures, and highlights different types of nodes, accordingly to its definition.

Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration. FRS are defined as the set of nodes that can be reached from an initial seed via a path of temporally ordered edges; a natural extension of connected component measures to dynamic networks. Working in a stochastic framework, we derive closed-form expressions for the mean and variance of the exponential growth rate of the FRS for temporal networks with both edge and node dynamics. For networks with node dynamics, we calculate thresholds for the growth of the FRS. The effects of finite population size are explored via simulation and approximation. We examine how these properties vary by edge duration and different cross-sectional degree distributions that characterize a range of scientifically interesting normative outcomes (Poisson and Bernoulli). The size of the forward reachable set gives an upper bound for the epidemic size in disease transmission network models, relating this work to epidemic modeling (Ferguson, 2000; Eames, 2004).