We propose a novel tie-oriented model for longitudinal event network data. The generating mechanism is assumed to be a multivariate Poisson process that governs the onset and repetition of yearly observed events with two separate intensity functions. We apply the model to a network obtained from the yearly dyadic number of international deliveries of combat aircraft trades between 1950 and 2017. Based on the trade gravity approach, we identify economic and political factors impeding or promoting the number of transfers. Extensive dynamics as well as country heterogeneities require the specification of semiparametric time-varying effects as well as random effects. Our findings reveal strong heterogeneous as well as time-varying effects of endogenous and exogenous covariates on the onset and repetition of aircraft trade events.

With origins in post-war development thinking, the core–periphery concept has spread across the social and, increasingly, the natural sciences. Initially reflecting divergent socioeconomic properties of geographical regions, its relational connotations rapidly led to more topological interpretations. In today's network science, the standard core–periphery model consists of a cohesive set of core actors and a peripheral set of internally disconnected actors. Exploring the classical core–periphery literature, this paper finds conceptual support for the characteristic intra-categorical density differential. However, this literature also lends support to the notions of peripheral dependency and core dominance, power-relational aspects that existing approaches do not capture. To capture such power-relations, this paper suggests extensions to the correlation-based core–periphery metric of Borgatti and Everett (2000). Capturing peripheral dependency and, optionally, core dominance, these extensions allow for either measuring the degree of such power-relational features in given core–periphery partitions, or as part of a criteria function to search for power-relational core–periphery structures. Applied to the binary and valued citation data in Borgatti and Everett (2000), the proposed extensions seemingly capture dependency and dominance features of core–periphery structures. This is particularly evident when, circling back to the original domains of the concept, examining the network of European commodity trade in 2010.

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural features. These features tend to be shared by networks belonging to the same broad class, such as the class of social networks or the class of biological networks. Within each such class, networks describing similar systems tend to have similar features. This occurs presumably because networks representing similar systems would be expected to be generated by a shared set of domain-specific mechanisms, and it should therefore be possible to classify networks based on their features at various structural levels. Here we describe and demonstrate a new hybrid approach that combines manual selection of network features of potential interest with existing automated classification methods. In particular, selecting well-known network features that have been studied extensively in social network analysis and network science literature, and then classifying networks on the basis of these features using methods such as random forest, which is known to handle the type of feature collinearity that arises in this setting, we find that our approach is able to achieve both higher accuracy and greater interpretability in shorter computation time than other methods.

Reciprocity—the mutual provisioning of support/goods—is a pervasive feature of social life. Directed networks provide a way to examine the structure of reciprocity in a community. However, measuring social networks involves assumptions about what relationships matter and how to elicit them, which may impact observed reciprocity. In particular, the practice of aggregating multiple sources of data on the same relationship (e.g., “double-sampled” data, where both the “giver” and “receiver” are asked to report on their relationship) may have pronounced impacts on network structure. To investigate these issues, we examine concordance (ties reported by both parties) and reciprocity in a set of directed, double-sampled social support networks. We find low concordance in people’s responses. Taking either the union (including any reported ties) or the intersection (including only concordant ties) of double-sampled relationships results in dramatically higher levels of reciprocity. Using multilevel exponential random graph models of social support networks from 75 villages in India, we show that these changes cannot be fully explained by the increase in the number of ties produced by layer aggregation. Respondents’ tendency to name the same people as both givers and receivers of support plays an important role, but this tendency varies across contexts and relationships type. We argue that no single method should necessarily be seen as the “correct” choice for aggregation of multiple sources of data on a single relationship type. Methods of aggregation should depend on the research question, the context, and the relationship in question.

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.

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.

City road networks have been extensively studied for their social significance or to quantify their connections and centralities, but often their geographical origin is forgotten. This work focuses on the spatial-geographical and geometrical aspects of the road network skeleton. Following previous work, a multi-scale object, the way, is constructed, based only on the local geometry at road crossings. The best method to reconstruct significant elements is investigated. The results show that this object is geographically meaningful, with many particular characteristics. A new indicator, structurality, is introduced and compared with previous indicators, on the cities of Paris and Avignon. Structurality appears to be stable over the borders of the map sample, and is able to reveal the underlying coherence of the road network. This stability can be interpreted as coming from the particular way the network developed in time, and was later preserved. This link with the historical development of the cites, which deserves to be further studied, is exemplified in the cases of Villers-sur-Mer (France) and Manaus (Brazil). The construction method, the results, and their potential meaning are discussed in detail so that they can be used in various related disciplines, such as sociology, town planning, geomatics, and physics.

Today's economy, production activity, and our life are sustained by social and technological network infrastructures, while new threats of network attacks by destructing loops have been found recently in network science. We inversely take into account the weakness, and propose a new design principle for incrementally growing robust networks. The networks are self-organized by enhancing interwoven long loops. In particular, we consider the range-limited approximation of linking by intermediations in a few hops, and show the strong robustness in the growth without degrading efficiency of paths. Moreover, we demonstrate that the tolerance of connectivity is reformable even from extremely vulnerable real networks according to our proposed growing process with some investment. These results may indicate a prospective direction to the future growth of our network infrastructures.

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).

Real world networks typically have large clustering coefficients. The clustering coefficient can be interpreted to be the result of a triangle closing mechanism. We have here enumerated cliques and maximal cliques in multiple networks to show that real world networks have a high number of large cliques. While triangles are more frequent than expected, large cliques are much more over-expressed, and the largest difference between real world networks and their random counterpart occurs in many networks at clique sizes of 5–7, and not at a size of 3. This does not result from the existence of few very large cliques, since a similar feature is observed when studying only maximal cliques (cliques that are not contained in other larger cliques). Moreover, when the large cliques are removed, triangles are often under-expressed.

In all networks studied but one, all node members of large cliques produce a single connected component, which represent the central “core” of the network. The observed clique distribution can be explained by multiple models, mainly hidden variables model, such as the gravitation model, or the collapse of bipartite networks. These models can explain other properties of these networks, including the sub-graph distribution and the distance distribution of the networks. This suggests that node connectivity in real world networks may be determined by the similarity between the contents of the networks' nodes. This is in contrast with models of network formation that incorporate only the properties of the network, and not the internal properties of the nodes.

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.

We used in-depth interviews with 101 participants in the East York section of Toronto, Canada to understand how digital media affects social connectivity in general—and networked individualism in particular—for people at different stages of the life course. Although people of all ages intertwined their use of digital media with their face-to-face interactions, younger adults used more types of digital media and have more diversified personal networks. People in different age-groups conserved media, tending to stick with the digital media they learned to use in earlier life stages. Approximately one-third of the participants were Networked Individuals: In each age-group, they were the most actively using digital media to maintain ties and to develop new ones. Another one-third were Socially Bounded, who often actively used digital media but kept their connectivity within a smaller set of social groups. The remaining one-third, who were Socially Limited, were the least likely to use digital media. Younger adults were the most likely to be Networked Individuals, leading us to wonder if the percentage of the population who are Bounded or Limited will decline over time.

International trade has been increasingly organized in the form of global value chains (GVCs). In this paper, we provide a new method for comparing GVCs across countries and over time. First, we use the World Input–Output Database (WIOD) to construct both the upstream and the downstream global value networks. Second, we introduce a network-based measure of node similarity to compare the GVCs between any pair of countries for each sector and each year available in the WIOD. Our network-based similarity is a better measure for node comparison than the existing ones because it takes into account all the direct and indirect relationships between the country–sector pairs, is applicable to both directed and weighted networks with self-loops, and takes into account externally defined node attributes. As a result, our measure of similarity reveals the most intensive interactions among the GVCs across countries and over time. From 1995 to 2011, the average similarity between sectors and countries have clear increasing trends, which are temporarily interrupted by the recent economic crisis. This measure of the similarity of GVCs provides quantitative answers to important questions about dependency, sustainability, risk, and competition in the global production system.

This paper investigates the distributions of triangle counts per vertex and edge, as a means for network description, analysis, model building, and other tasks. The main interest is in estimating these distributions through sampling, especially for large networks. A novel sampling method tailored for the estimation analysis is proposed, with three sampling designs motivated by several network access scenarios. An estimation method based on inversion and an asymptotic method are developed to recover the entire distribution. A single method to estimate the distribution using multiple samples is also considered. Algorithms are presented to sample the network under the various access scenarios. Finally, the estimation methods on synthetic and real-world networks are evaluated in a data study.

We review the empirical comparison of Stochastic Actor-oriented Models (SAOMs) and Temporal Exponential Random Graph Models (TERGMs) by Leifeld & Cranmer in this journal [Network Science 7(1):20–51, 2019]. When specifying their TERGM, they use exogenous nodal attributes calculated from the outcome networks’ observed degrees instead of endogenous ERGM equivalents of structural effects as used in the SAOM. This turns the modeled endogeneity into circularity and obtained results are tautological. In consequence, their out-of-sample predictions using TERGMs are based on out-of-sample information and thereby predict the future using observations from the future. Thus, their analysis rests on erroneous model specifications that invalidate the article’s conclusions. Finally, beyond these specific points, we argue that their evaluation metric—tie-level predictive accuracy—is unsuited for the task of comparing model performance.

Latent stochastic blockmodels are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between nodes are observed at a number of different times. In this paper, we propose a new Bayesian framework to characterize the construction of connections. We rely on a Markovian property to describe the evolution of nodes' cluster memberships over time. We recast the problem of clustering the nodes of the network into a model-based context, showing that the integrated completed likelihood can be evaluated analytically for a number of likelihood models. Then, we propose a scalable greedy algorithm to maximize this quantity, thereby estimating both the optimal partition and the ideal number of groups in a single inferential framework. Finally, we propose applications of our methodology to both real and artificial datasets.

The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs–Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature T) controlling the entropic level of the distribution. This formalism enables the computation of new distances or dissimilarities, interpolating between the shortest-path and the resistance distance, which have been shown to perform well in clustering and classification tasks. In this work, the bag-of-paths formalism is extended by adding two independent equality constraints fixing starting and ending nodes distributions of paths (margins).When the temperature is low, this formalism is shown to be equivalent to a relaxation of the optimal transport problem on a network where paths carry a flow between two discrete distributions on nodes. The randomization is achieved by considering free energy minimization instead of traditional cost minimization. Algorithms computing the optimal free energy solution are developed for two types of paths: hitting (or absorbing) paths and non-hitting, regular, paths and require the inversion of an n × n matrix with n being the number of nodes. Interestingly, for regular paths on an undirected graph, the resulting optimal policy interpolates between the deterministic optimal transport policy (T → 0+) and the solution to the corresponding electrical circuit (T → ∞). Two distance measures between nodes and a dissimilarity between groups of nodes, both integrating weights on nodes, are derived from this framework.

Social relationships are important among persons experiencing homelessness, but there is little research on changes in social networks among persons moving into permanent supportive housing (PSH). Using data collected as part of a longitudinal study of 405 adults (aged 39+) moving into PSH, this study describes network upheaval during this critical time of transition. Interviews conducted prior to and after three months of living in PSH assessed individual-level (demographics, homelessness history, health, and mental health) and social network characteristics, including network size and composition (demographics, relationship type, and social support). Interviewers utilized network member characteristics to assess whether network members were new or sustained between baseline and three months post-housing. Multilevel logistic regression models assessed characteristics of network members associated with being newly gained or persisting in networks three months after PSH move-in. Results show only one-third of social networks were retained during the transition to PSH, and veterans, African Americans, and other racial/ethnic minorities, and those living in scattered site housing, were more likely to experience network disruption. Relatives, romantic partners, and service providers were most likely to be retained after move-in. Some network change was moderated by tie strength, including the retention of street-met persons. Implications are discussed.

We introduce a weighted configuration model graph, where edge weights correspond to the probability of infection in an epidemic on the graph. On these graphs, we study the development of a Susceptible–Infectious–Recovered epidemic using both Reed–Frost and Markovian settings. For the special case of having two different edge types, we determine the basic reproduction numberR0, the probability of a major outbreak, and the relative final size of a major outbreak. Results are compared with those for a calibrated unweighted graph. The degree distributions are based on both theoretical constructs and empirical network data. In addition, bivariate standard normal copulas are used to model the dependence between the degrees of the two edge types, allowing for modeling the correlation between edge types over a wide range. Among the results are that the weighted graph produces much richer results than the unweighted graph. Also, while R0 always increases with increasing correlation between the two degrees, this is not necessarily true for the probability of a major outbreak nor for the relative final size of a major outbreak. When using copulas we see that these can produce results that are similar to those of the empirical degree distributions, indicating that in some cases a copula is a viable alternative to using the full empirical data.