Measures of bipartite network structure have recently gained attention from network scholars. However, there is currently no measure for identifying key players in two-mode networks. This article proposes measures for identifying key players in bipartite networks. It focuses on two measures: fragmentation and cohesion centrality. It extends the centrality measures to bipartite networks by considering (1) cohesion and fragmentation centrality within a one-mode projection, (2) cross-modal cohesion and fragmentation centrality, where a node in one mode is influential in the one-mode projection of the other mode, and (3) cohesion and fragmentation centrality across the entire bipartite structure. Empirical examples are provided for the Southern Women’s data and on the Ndrangheta mafia data.

We consider the problem of generating uniformly random graphs from a constrained distribution. A graph is valid if it obeys certain constraints such as a given number of nodes, edges, k-stars or degree sequence, and each graph must occur with equal probability. A typical application is to confirm the correctness of a model by repeated sampling and comparing statistical properties against empirical data. Markov Chain Monte Carlo (MCMC) algorithms are often used, but have certain difficulties such as the inability to search the space of all possible valid graphs. We propose an improved algorithm which overcomes these difficulties. Although each individual iteration of the MCMC algorithm takes longer, we obtain better coverage of the search space in the same amount of time. This leads to better estimates of various quantities such as the expected number of transitive triads given the constraints. The algorithm should be of general interest with many possible applications, including the world wide web, biological, and social networks.

Social networks, particularly those defined by friendships, influence many childhood and adolescent health behaviors such as the use of alcohol, tobacco, and other drugs, as well as diet and physical activity. Few, if any, studies have examined the concordance between friendship networks and sun exposure/safety behaviors. This study examines the friendship networks and sun safety behaviors for a group of fourth and fifth grade students taking part in a larger sun safety intervention, “SunSmart” (n = 128). Intra-class correlation, homophily hypothesis testing, and exponential random graph models were used to test friendship homophily based on sun safety behaviors. Peer Leaders were identified through social network popularity, and sun safety change scores were compared between Peer Leaders and non-leaders. Results show that students cluster based on shared demographic characteristics and some sun safety behaviors, and that there was a trend for Peer Leaders to respond better to the SunSmart intervention than non-leaders. Implications for future sun safety interventions using Peer Leaders as champions for sun safety behavior change are discussed.

While network research often focuses on social integration as a predictor of health, a less-explored idea is that connections to dissimilar others may benefit well-being. As such, this study investigates whether network diversity is associated with changes in four health outcomes over a 3-year period of time in the U.S.A. Specifically, we focus on how an underexplored measure of network diversity—educational attainment assortativity—is associated with common self-reported outcomes: propensity to exercise, body-mass index, mental health, and physical health. We extend prior research by conducting multilevel analyses using this measure of diversity while adjusting for a range of socio-demographic and network confounders. Data are drawn from a longitudinal probability sample of U.S. adults (n=10.679) in which respondents reported information about themselves and eight possible alters during three yearly surveys (2013–2015). We find, first, that higher educational attainment is associated with more educationally insular networks, while less-educated adults have more educationally diverse networks. Results further suggest that having educationally similar networks is associated with higher body-mass index among the less educated. Further exploration of the relationship between ego network diversity, tie strength, and health is warranted.

Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.

The topic of anomaly detection in networks has attracted a lot of attention in recent years, especially with the rise of connected devices and social networks. Anomaly detection spans a wide range of applications, from detecting terrorist cells in counter-terrorism efforts to identifying unexpected mutations during ribonucleic acid transcription. Fittingly, numerous algorithmic techniques for anomaly detection have been introduced. However, to date, little work has been done to evaluate these algorithms from a statistical perspective. This work is aimed at addressing this gap in the literature by carrying out statistical evaluation of a suite of popular spectral methods for anomaly detection in networks. Our investigation on the statistical properties of these algorithms reveals several important and critical shortcomings that we make methodological improvements to address. Further, we carry out a performance evaluation of these algorithms using simulated networks and extend the methods from binary to count networks.

We consider a dynamic network cascade process developed by Duncan Watts applied to a class of random networks, developed independently by Newman and Miller, which allows a specified amount of clustering (short loops). We adapt existing methods for locally tree-like networks to formulate an appropriate two-type branching process to describe the spread of a cascade started with a single active node and obtain a fixed-point equation to implicitly express the extinction probability of such a cascade. In so doing, we also recover a formula that has appeared in various forms in works by Hackett et al. and Miller which provides a threshold condition for certain extinction of the cascade. We find that clustering impedes cascade propagation for networks of low average degree by reducing the connectivity of the network, but for networks with high average degree, the presence of small cycles makes cascades more likely.

Hyperbolic random graphs (HRGs) and geometric inhomogeneous random graphs (GIRGs) are two similar generative network models that were designed to resemble complex real-world networks. In particular, they have a power-law degree distribution with controllable exponent $\beta$ and high clustering that can be controlled via the temperature $T$ .

We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to $T = 0$ . We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, that is, they involve no approximation.

Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the desired expected average degree as input.

Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straightforward inclusion does not hold in practice. However, the difference is negligible for most use cases.

Does the human brain have a central connective core, and, if so, how costly is it?

Noninvasive imaging data allow the construction of network maps of the human brain, recording its structural and functional connectivity. A number of studies have reported on various characteristic network attributes, such as a tendency toward local clustering, high global efficiency, the prevalence of specific network motifs, and a pronounced community structure with several anatomically and functionally defined modules and interconnecting hub regions (Bullmore & Sporns, 2009; van den Heuvel & Hulshoff Pol, 2010; Sporns, 2011). Hubs are of particular interest in studies of the brain since they may play crucial roles in integrative processes and global brain communication, thought to be essential for many aspects of higher brain function. Indeed, hubs have been shown to correspond to brain regions that exhibit complex physiological responses and maintain widespread and diverse connection profiles with other parts of the brain. We asked if, in addition to being highly connected, brain hubs would also exhibit a strong tendency to be mutually interconnected, forming what has been called a “rich club” (Colizza et al., 2006). Rich club organization is present in a network if sets of high-degree nodes exhibit denser mutual connections than predicted on the basis of the degree sequence alone. We investigated rich club organization in the human brain in datasets that recorded weighted projections among different anatomical regions of the cerebral cortex, recorded from several cohorts of healthy human volunteers (van den Heuvel & Sporns, 2011; van den Heuvel et al., 2012).

This study considered the role of adult children in the core networks of U.S. older adults with varying levels of functional health. Taking a multidimensional perspective of the ego network system, we considered (a) presence of child(ren) in the network, (b) contact with children network members, and (c) embeddedness of children within the network. We observed older parents from three waves of the National Social Life, Health, and Aging Project (NSHAP). The common ‘important matters’ name generator was used to construct egocentric network variables, while self-reported difficulty with activities of daily life was used to measure disablement transitions. Parameters were estimated with Generalized Estimating Equations (GEE). Though child turnover was common in parents’ core networks, there was no evidence linking disablement transitions to systematic forms of child reshuffling. Children that remained in parents’ networks, however, showed increased contact with parents and with other members of the network when the parent underwent disability progression. Disability onset was not significantly linked to either outcome. There was limited evidence of gender variation in these patterns. Overall, results strengthen the view that children are distinctive members of older adults’ core networks. Further, the role of adult children shifts most noticeably at advanced stages of the disablement process.

Genetic risk is particularly salient for families and testing for genetic conditions is necessarily a family-level process. Thus, risk for genetic disease represents a collective stressor shared by family members. According to communal coping theory, families may adapt to such risk vis-a-vis interpersonal exchange of support resources. We propose that communal coping is operationalized through the pattern of supportive relationships observed between family members. In this study, we take a social network perspective to map communal coping mechanisms to their underlying social interactions and include those who declined testing or were not at risk for Lynch Syndrome. Specifically, we examine the exchange of emotional support resources in families at risk of Lynch Syndrome, a dominantly inherited cancer susceptibility syndrome. Our results show that emotional support resources depend on the testing-status of individual family members and are not limited to the bounds of the family. Network members from within and outside the family system are an important coping resource in this patient population. This work illustrates how social network approaches can be used to test structural hypotheses related to communal coping within a broader system and identifies structural features that characterize coping processes in families affected by Lynch Syndrome.

We describe here a notion of diffusion similarity, a method for defining similarity between vertices in a given graph using the properties of random walks on the graph to model the relationships between vertices. Using the approach of graph vertex embedding, we characterize a vertex vi by considering two types of diffusion patterns: the ways in which random walks emanate from the vertex vi to the remaining graph and how they converge to the vertex vi from the graph. We define the similarity of two vertices vi and vj as the average of the cosine similarity of the vectors characterizing vi and vj. We obtain these vectors by modifying the solution to a differential equation describing a type of continuous time random walk.

This method can be applied to any dataset that can be assigned a graph structure that is weighted or unweighted, directed or undirected. It can be used to represent similarity of vertices within community structures of a network while at the same time representing similarity of vertices within layered substructures (e.g., bipartite subgraphs) of the network. To validate the performance of our method, we apply it to synthetic data as well as the neural connectome of the C. elegans worm and a connectome of neurons in the mouse retina. A tool developed to characterize the accuracy of the similarity values in detecting community structures, the uncertainty index, is introduced in this paper as a measure of the quality of similarity methods.

This article considers the link removal problem in a strongly connected directed network with the goal of minimizing the dominant eigenvalue of the network’s adjacency matrix while maintaining its strong connectivity. Due to the complexity of the problem, this article focuses on computing a suboptimal solution. Furthermore, it is assumed that the knowledge of the overall network topology is not available. This calls for distributed algorithms which rely solely on the local information available to each individual node and information exchange between each node and its neighbors. Two different strategies based on matrix perturbation analysis are presented, namely simultaneous and iterative link removal strategies. Key ingredients in implementing both strategies include novel distributed algorithms for estimating the dominant eigenvectors of an adjacency matrix and for verifying strong connectivity of a directed network under link removal. It is shown via numerical simulations on different type of networks that in general the iterative link removal strategy yields a better suboptimal solution. However, it comes at a price of higher communication cost in comparison to the simultaneous link removal strategy.

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.

This paper investigates the processes involved when newly hired employees need to simultaneously build up and mobilize personal network ties during their organizational socialization. It focuses on the quality of ties at an early formative stage, characterized by the lack of a tie history between actors. Social capital theory would suggest that such nascent ties do not offer optimal channels for the kind and volume of resources that newcomers (need to) rely on during socialization. To better understand how this apparent mismatch between tie quality and resource needs is handled from an ego-centered perspective, the paper analyzes personal network data from 24 newcomers in nine organizations, using an adapted form of Qualitative Structural Analysis. Three tie-level qualities are found to explain how the lack of tie history may be alleviated, circumvented, or compensated. They comprise (a) variants of openness experienced with stronger ties, (b) perceptions of a lowered threshold towards weaker ties, and (c) sources of legitimacy regarding latent ties. Based on these findings, the paper presents an integrated conceptual model to clarify how nascent ties offer channels for network resources during socialization and discusses the need for further research on the role of specific moderators for the investigated processes.

Social networks, wherein the edges represent nonbehavioral relations such as friendship, power, and influence, can be difficult to measure and model. A powerful tool to address this is cognitive social structures (Krackhardt, D. (1987). Cognitive social structures. Social Networks, 9(2), 109–134.), where the perception of the entire network is elicited from each actor. We provide a formal statistical framework to analyze informants’ perceptions of the network, implementing a latent space network model that can estimate, e.g., homophilic effects while accounting for informant error. Our model allows researchers to better understand why respondents’ perceptions differ. We also describe how to construct a meaningful single aggregated network that ameliorates potential respondent error. The proposed method provides a visualization method, an estimate of the informants’ biases and variances, and we describe a method for sidestepping forced-choice designs.

Many classic networks grow by hooking small components via vertices. We introduce a class of networks that grows by fusing the edges of a small graph to an edge chosen uniformly at random from the network. For this random edge-hooking network, we study the local degree profile, that is, the evolution of the average degree of a vertex over time. For a special subclass, we further determine the exact distribution and an asymptotic gamma-type distribution. We also study the “core,” which consists of the well-anchored edges that experience fusing. A central limit theorem emerges for the size of the core.

At the end, we look at an alternative model of randomness attained by preferential hooking, favoring edges that experience more fusing. Under preferential hooking, the core still follows a Gaussian law but with different parameters. Throughout, Pólya urns are systematically used as a method of proof.

The special issue of “Networks in space and in time: methods and applications” contributes to the debate on contextual analysis in network science. It includes seven research papers that shed light on the analysis of network phenomena studied within geographic space and across temporal dimensions. In these papers, methodological issues as well as specific applications are described from different fields. We take the seven papers, study their citations and texts, and relate them to the broader literature. By exploiting the bibliographic information and the textual data of these seven documents, citation analysis and lexical correspondence analysis allow us to evaluate the connections among the papers included in this issue.

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.