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.

We compare and contrast the network formation of interest groups across industry and issue area. We focus on membership interest groups, which by virtue of representing the interests of voluntary members face particular organizational and maintenance constraints. To reveal their cooperative behavior we build a network dataset based on cosigner status to United States Supreme Court amicus curiae briefs and analyze it with exponential random graph models and multidimensional scaling. Our methodological approach culminates in a clear and compact spatial representation of network similarities and differences. We find that while many of the same factors shape membership networks, religious, labor, and political organizations do not share the same structure as each other or as the business, civic and professional groups.

Centralities are a widely studied phenomenon in network science. In policy networks, central actors are of interest because they are assumed to control information flows, to link opposing coalitions and to directly impact decision-making. First, we study what type of actor (e.g., state authorities or interest groups) is able to occupy central positions in the highly institutionalized context of policy networks. Second, we then ask whether bonding or bridging centralities prove to be more stable over time. Third, we investigate how these types of centrality influence actors’ positions in a network over time. We therefore adopt a longitudinal perspective and run exponential random graph models, including lagged central network positions at t1 as the main independent variable for actors’ activity and popularity at t2. Results confirm that very few actors are able to maintain central positions over time.

Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more. Modularity is a quality function that measures the difference between the number of edges found within clusters minus the number of edges one would statistically expect to find based on some equivalent random graph model. We explore a natural generalization of modularity based on the difference between the actual and expected number of walks within clusters, which we refer to as walk-modularity. Walk-modularity can be expressed in matrix form, and community detection can be performed by finding the leading eigenvector of the walk-modularity matrix. We demonstrate community detection on both synthetic and real-world networks and find that walk-modularity maximization returns significantly improved results compared to traditional modularity maximization.

Despite the pivotal role that both power and interpersonal trust play in a multitude of social exchange situations, relatively little is known about their interplay. Moreover, previous theorizing makes competing claims. Do we consider our relatively more powerful exchange partners to be less trustworthy, as rational choice reasoning would suggest? Or do more complex psychological mechanisms lead us to trust them more, as motivated cognition reasoning implies? Extending the latter approach, we develop and empirically test three hypotheses on the interrelation between perceptions of interpersonal trust and power. According to the status value hypothesis, individuals are more likely to befriend those whom they or others perceive as powerful. The status signaling hypothesis states that the friends of people one perceives as powerful will also be seen as powerful. According to the self-monitoring hypothesis, high self-monitors are more likely than low self-monitors to befriend those they or others perceive as powerful. We use multiplex stochastic actor-based models to analyze the co-evolution of trust and power relations among n = 49 employees in a Dutch Youth Care organization. Data covers three waves of a longitudinal sociometric network survey collected over a period of 18 months in the years 2009–2010. In general, we find some support for all three hypotheses, though the effects are weak. Being one of the first organizational field studies on the co-evolution of power and trust, we conclude with discussing the implications of these findings for the study of social exchange processes.

This paper presents a variable neighborhood search (VNS) algorithm that is specially designed for the blockmodeling of two-mode binary network matrices in accordance with structural equivalence. Computational results for 768 synthetic test networks revealed that the VNS heuristic outperformed a relocation heuristic (RH) and a tabu search (TS) method for the same problem. Next, the three heuristics were applied to two-mode network data pertaining to the votes of member countries on resolutions in the United Nations General Assembly. A comparative analysis revealed that the VNS heuristic often provided slightly better criterion function values than RH and TS, and that these small differences in criterion function values could sometimes be associated with substantial differences in the actual partitions obtained. Overall, the results suggest that the VNS heuristic is a promising approach for blockmodeling of two-mode binary networks. Recommendations for extensions to stochastic blockmodeling applications are provided.

We assess the potential of network motif profiles to characterize ego-networks in much the same way that a bag-of-words strategy allows text documents to be compared in a vector space framework. This is potentially valuable as a generic strategy for comparing nodes in a network in terms of the network structure in which they are embedded. In this paper, we consider the computational challenges and model selection decisions involved in network motif profiling. We also present three case studies concerning the analysis of Wikipedia edit networks, YouTube spam campaigns, and peer-to-peer lending in the Prosper marketplace.

Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic information-theoretic relative performance of Laplacian spectral embedding and adjacency spectral embedding for block assignment recovery in stochastic blockmodel graphs by way of Chernoff information. We investigate the relationship between spectral embedding performance and underlying network structure (e.g., homogeneity, affinity, core-periphery, and (un)balancedness) via a comprehensive treatment of the two-block stochastic blockmodel and the class of K-blockmodels exhibiting homogeneous balanced affinity structure. Our findings support the claim that, for a particular notion of sparsity, loosely speaking, “Laplacian spectral embedding favors relatively sparse graphs, whereas adjacency spectral embedding favors not-too-sparse graphs.” We also provide evidence in support of the claim that “adjacency spectral embedding favors core-periphery network structure.”

Trade in oil has undergone significant changes in the last 20 years: technical progress has allowed the exploitation of new and previously untapped fields; the emergence of new large oil importers, such as China, has shifted the traditional patterns of demand and supply, while the desire to diversify energy sources has favored the emergence of new suppliers. This paper compares the topological properties of the network of crude oil trade over the period 1995–2014. The analysis covers both aggregate measures (such as network density and centralization) and node-specific indicators (e.g. centrality) that allow to uncover the rise (demise) of new (old) important players. Accounting for the position of each country within the network provides valuable information above and beyond traditional measures such as market shares. To investigate whether oil trade has experienced a process of globalization or, rather, regionalization, we look at the community structure of the network: the number of communities increases in the aftermath of the global financial crisis, but then goes back to its historical values. Something similar happens to the average geographic distance within each community, showing that along a regional component there are also strategic/political considerations at play. Econometric analysis suggests that high oil prices increase the likelihood that high-production-cost exporters play a more central role in the network, thus reducing the power of traditional suppliers.

An incredible number of centrality indices has been proposed to date (Todeschini & Consonni, 2009). Four of them, however, can be considered prototypical because they operationalize distinct concepts of centrality and together cover the bulk of analyses and empirical uses: degree, closeness, betweenness, and eigenvector centrality.

Mobile phones are spreading to remote areas of the globe, leading to the following question: “What is the potential of the new communication technologies for increasing individuals' access to information and the diffusion of attitudes and practices across rural areas of developing countries?” We have donated phones to 234 farmers selected by stratified random sampling in an agrarian region of Ethiopia and have tracked their main communication partners for six months. The panel data and qualitative interviews indicated that the phones were not typically used to expand the existing constrained social networks or to gain information from new sources but to call contacts who had been known personally and to individuals introduced through the experiment. Stochastic actor-based network models clarified that although agricultural information-seeking and casual calling are intertwined, the mechanisms underlying the evolution of instrumental and expressive communication networks are distinct. Acquaintances living beyond comfortable walking distances and individuals whom others call became preferred for information-seeking calls. Thus, mobile phones may accelerate information exchange within existing social networks and may support the creation of new information hubs that might facilitate more efficient information diffusion over long distances in the future. In contrast, the importance of geographical communities strongly prevails in casual phone conversations. Physically proximate community members who tend to be met frequently were preferred for sentiment-sharing calls. Preferential attachment was not evident for this type of communication. As a result, the network of these expressive calls was highly localized and fragmented, making it unlikely for personal feelings to diffuse across wide geographical areas through the new phone networks.

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.

Social network analysis is the study of how links between a set of actors are formed. Typically, it is believed that links are formed in a structured manner, which may be due to, for example, political or material incentives, and which often may not be directly observable. The stochastic blockmodel represents this structure using latent groups which exhibit different connective properties, so that conditional on the group membership of two actors, the probability of a link being formed between them is represented by a connectivity matrix. The mixed membership stochastic blockmodel extends this model to allow actors membership to different groups, depending on the interaction in question, providing further flexibility.

Attribute information can also play an important role in explaining network formation. Network models which do not explicitly incorporate covariate information require the analyst to compare fitted network models to additional attributes in a post-hoc manner. We introduce the mixed membership of experts stochastic blockmodel, an extension to the mixed membership stochastic blockmodel which incorporates covariate actor information into the existing model. The method is illustrated with application to the Lazega Lawyers dataset. Model and variable selection methods are also discussed.

This paper examines the stability of egocentric networks as reported over time using a novel touchscreen-based participant-aided sociogram. Past work has noted the instability of nominated network alters, with a large proportion leaving and reappearing between interview observations. To explain this instability of networks over time, researchers often look to structural embeddedness, namely the notion that alters are connected to other alters within egocentric networks. Recent research has also asked whether the interview situation itself may play a role in conditioning respondents to what might be the appropriate size and shape of a social network, and thereby which alters ought to be nominated or not. We report on change in these networks across three waves and assess whether this change appears to be the result of natural churn in the network or whether changes might be the result of factors in the interview itself, particularly anchoring and motivated underreporting. Our results indicate little change in average network size across waves, particularly for indirect tie nominations. Slight, significant changes were noted between waves one and two particularly among those with the largest networks. Almost no significant differences were observed between waves two and three, either in terms of network size, composition, or density. Data come from three waves of a Chicago-based panel study of young men who have sex with men.

We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particular, the proposed curvatures based on the interpretation of Haantjes definition as geodesic curvature allow us to give a network analogue of the classical local Gauss–Bonnet theorem. Furthermore, we propose even simpler and more intuitive proxies for the Haantjes curvature that allow for even faster and easier computations in large-scale networks. In addition, we also investigate the embedding properties of the proposed Ricci curvatures. Lastly, we also investigate the behavior, both on model and real-world networks, of the curvatures introduced herein with more established notions of Ricci curvature and other widely used network measures.

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).

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.

Recent work studying triadic closure in undirected graphs has drawn attention to the distinction between measures that focus on the “center” node of a wedge (i.e., length-2 path) versus measures that focus on the “initiator,” a distinction with considerable consequences. Existing measures in directed graphs, meanwhile, have all been center-focused. In this work, we propose a family of eight directed closure coefficients that measure the frequency of triadic closure in directed graphs from the perspective of the node initiating closure. The eight coefficients correspond to different labeled wedges, where the initiator and center nodes are labeled, and we observe dramatic empirical variation in these coefficients on real-world networks, even in cases when the induced directed triangles are isomorphic. To understand this phenomenon, we examine the theoretical behavior of our closure coefficients under a directed configuration model. Our analysis illustrates an underlying connection between the closure coefficients and moments of the joint in- and out-degree distributions of the network, offering an explanation of the observed asymmetries. We also use our directed closure coefficients as predictors in two machine learning tasks. We find interpretable models with AUC scores above 0.92 in class-balanced binary prediction, substantially outperforming models that use traditional center-focused measures.

Students’ personal learning networks can be a valuable resource of success in higher education: they offer opportunities for academic and personal support and provide sources of information related to exams or homework. We study the determinants of learning networks using a panel study among university students in their first and second year of study. A long-standing question in social network analysis has been whether the tendency of individuals with similar characteristics to form ties is a result of preferences “choice homophily” or rather selective opportunities “induced homophily”. We expect a latent preference for homophilic learning partnerships with regard to attributes, such as gender, ability, and social origin. We estimate recently developed temporal exponential random graph models to control for previous network structure and study changes in learning ties among students. The results show that especially for males, same-gender partnerships are preferred over heterogeneous ties, while chances for tie formation decrease with the difference in academic ability among students. Social origin is a significant factor in the crosssectional exploration but does appear to be less important in the formation of new (strong) partnerships during the course of studies.

This study documents historical trends of size and political diversity in Americans’ discussion networks, which are often seen as important barometers of social and political health. Contrasting findings from data drawn out of a nationally representative survey experiment of 1,055 Americans during the contentious 2016 U.S. presidential election to data arising from 11 national data sets covering nearly three decades, we find that Americans’ core networks are significantly smaller and more politically homogeneous than at any other period. Several methodological artifacts seem unlikely to account for the effect. We show that in this period, more than before, “important matters” were often framed as political matters, and that this association probably accounts for the smaller networks.