Most network studies rely on a measured network that differs from the underlying network which is obfuscated by measurement errors. It is well known that such errors can have a severe impact on the reliability of network metrics, especially on centrality measures: a more central node in the observed network might be less central in the underlying network. Previous studies have dealt either with the general effects of measurement errors on centrality measures or with the treatment of erroneous network data. In this paper, we propose a method for estimating the impact of measurement errors on the reliability of a centrality measure, given the measured network and assumptions about the type and intensity of the measurement error. This method allows researchers to estimate the robustness of a centrality measure in a specific network and can, therefore, be used as a basis for decision-making. In our experiments, we apply this method to random graphs and real-world networks. We observe that our estimation is, in the vast majority of cases, a good approximation for the robustness of centrality measures. Beyond this, we propose a heuristic to decide whether the estimation procedure should be used. We analyze, for certain networks, why the eigenvector centrality is less robust than, among others, the pagerank. Finally, we give recommendations on how our findings can be applied to future network studies.

The clustering coefficient is typically used as a measure of the prevalence of node clusters in a network. Various definitions for this measure have been proposed for the cases of networks having weighted edges which may or not be directed. However, these techniques consistently assume that only a subset of all possible edges is present in the network, whereas there are weighted networks of interest in which all possible edges are present, that is, complete weighted networks. For this situation, the concept of clustering is redefined, and computational techniques are presented for computing an associated clustering coefficient for complete weighted undirected or directed networks. The performance of this new definition is compared with that of current clustering definitions when extended to complete weighted networks.

Digital technologies have created the potential for new forms of organizing among geographically dispersed individuals by connecting their ideas across the time and space in complex multiteam systems (MTSs). Realizing this potential requires novel forms of shared leadership structures to shepherd divergent and convergent thinking necessary to nurture innovation. While there is limited research on how space influences leadership and how the time influences leadership, there is virtually no theorizing on how space and time interact together to influence the emergence of shared leadership structures that facilitates innovation. A key contribution of this study is to utilize an agent-based model (ABM) that draws upon the research on leadership, networks, and innovation to specify generative mechanisms (or micro-processes) through which shared leadership structures emerge over space and time. The parameters in this model were estimated from empirical data. Results of virtual experiments (VE) yielded testable hypotheses suggesting that, over time, leadership capacity and between-team ties are negatively influenced by space. Furthermore, the computational model suggests that space increases the concentration of divergent leadership but decreases the concentration of convergent leadership. The study concludes by discussing the implications for the design of effective leadership structures to nurture innovation in MTSs.

Degree distribution is a fundamental property of networks. While mean degree provides a standard measure of scale, there are several commonly used shape measures. Widespread use of a single shape measure would enable comparisons between networks and facilitate investigations about the relationship between degree distribution properties and other network features. This paper describes five candidate measures of heterogeneity and recommends the Gini coefficient. It has theoretical advantages over many of the previously proposed measures, is meaningful for the broad range of distribution shapes seen in different types of networks, and has several accessible interpretations. While this paper focuses on degree, the distribution of other node-based network properties could also be described with Gini coefficients.

The spreading of transmissible infectious diseases is inevitably entangled with the dynamics of human population. Humans are the carrier of the pathogen, and the large-scale travel and commuting patterns that govern the mobility of modern societies are defining how epidemics and pandemics travel across the world. For a long time, the development of quantitative spatially explicit models able to shed light on the global dynamics of pandemic has been limited by the lack of detailed data on human mobility. In the last 10 years, however, these limits have been lifted by the increasing availability of data generated by new information technologies, thus triggering the development of computational (microsimulation) models working at a level of single individuals in spatially extended regions of the world. Microsimulations can provide information at very detailed spatial resolutions and down to the level of single individuals. In addition, computational implementations explicitly account for stochasticity, allowing the study of multiple realizations of epidemics with the same parameters' distribution. While on the one hand these capabilities represent the richness of microsimulation methods, on the other hand they face us with a huge amount of information that requires the use of specific data reduction methods and visual analytics.

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.

Asymmetric ties make up a significant proportion of ties in friendship networks. But little is known about their origins. Prior research has suggested treating them either as “accidental” (e.g., resulting from constraints in name generators) or “aspirational” (i.e., the attempts of individuals to pursue relationships with higher status peers). In this paper, we show that self-perception can also explain the occurrence of asymmetric ties. We argue that under the general norm of reciprocity, actors with high self-perceived centrality will more likely send out ties to others than their counterparts. Supposing that outgoing ties are similarly reciprocated by peers, then actors with high self-perceived centrality will also entail more asymmetric ties. We test this idea along with the competing arguments using exponential random graph models (ERGMs) on network data collected from over 4,000 students in China. Consistent with previous findings, we find that asymmetric ties reflect status differences, but probably more strongly so for difference in individual status characteristics than difference in social positional status. More importantly, we find that students with high self-perceived centrality are about twice as likely to send asymmetric ties as their peers. Last, we examine the implications of our findings for future network research.

Distributed information transfer is of paramount importance to the effectiveness of dynamic collective behaviors, especially when a swarm is confronted with complex environmental circumstances. Recently, the signaling network of interaction underlying such effective information transfers has been revealed in the particular case of bird flocks governed by a topological interaction. Such biological systems are known to be evolutionary optimized, but are also constrained by the very nature of the signaling mechanisms—owing to intrinsic limitations in sensory modalities—enabling communication among individuals. Here, we propose that artificial swarm design can be tackled from the angle of signaling network design. To this aim, we use different network models to investigate the impact of some network structural properties on the effectiveness of a specific emergent swarming behavior, namely global consensus. Two new network models are introduced, which together with the well-known Watts–Strogatz model form the basis for an analysis of the relationship between clustering, shortest path and speed to consensus. A network-theoretic approach combined with spectral graph theory tools are used to propose some signaling network design principles. Eventually, one key design principle—a concomitant reduction in clustering and connecting path—is successfully tested on simulations of swarms of self-propelled particles.

This paper explores the structural changes in the international organization of automotive production since the early 1990s. We apply descriptive network measures to international trade data for the period 1993–2013 for three automotive component groups with different technological intensity, with the aim of understanding (1) how the automotive international trade network has changed since the beginning of the 1990s; (2) whether regionalization has increased over time; (3) how the role that rising powers play within and between regions interacts with regionalization patterns. Our findings suggest that the structure of trade has changed significantly over the last two decades in all components. The network for electric and electrical parts and engines has evolved to become more hierarchical, with a cohesive core tied to hangers-on in the periphery, while the opposite has happened for rubber and metal. Regionalization patterns also show important differences across components. Finally, we have found an apparent association between the strengthening of regionalization patterns and the role played by traditional players and rising powers.

This study uses simulation over real and artificial networks to compare the eventual adoption outcomes of network interventions, operationalized as idealized contagion processes with different sets of seeds. While the performance depends on the details of both the network and behaviour adoption mechanisms, interventions with seeds that are central to the network are more effective than random selection in the majority of simulations, with faster or more complete adoption throughout the network. These results provide additional theoretical justification for utilizing relevant network information in the design of public health behavior interventions.

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.

Self-identification with peer crowds (jocks, popular kids, druggies, etc.) has an important influence on adolescent substance use behavior. However, little is known about the impact of the shared nature of crowd identification on different stages of adolescent drinking behavior, or the way crowd identification interacts with participation in school-sponsored sports activities. This study examines drinking influences from (1) peers with shared crowd identities, and (2) peers who jointly participate in organized sports at their school (activity members). This study introduces a new network analytic approach that can disentangle the effects of crowd identification and sports participation on individual behavior. Using survey data from adolescents in five high schools in a predominantly Hispanic/Latino district (N = 1,707), this paper examines the association between social influences and each stage of drinking behavior (intention to drink, lifetime, past-month, and binge drinking) by conducting an ordinal regression analysis. The results show that both shared identities and joint participation were associated with all stages of drinking, controlling for friends' influence. Additionally, shared identification overlapped with joint participation was associated with more frequent drinking. Related policy implications are discussed.

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives (Vespignani, 2009; Newman, 2010). A critical property of a network is its resilience to random breakdown and failure (Albert et al., 2000; Cohen et al., 2000; Callaway et al., 2000; Cohen et al., 2001), typically studied as a percolation problem (Stauffer & Aharony, 1994; Achlioptas et al., 2009; Chen & D'Souza, 2011) or by modeling cascading failures (Motter, 2004; Buldyrev et al., 2010; Brummitt, et al. 2012). Many complex systems, from power grids and the Internet to the brain and society (Colizza et al., 2007; Vespignani, 2011; Balcan & Vespignani, 2011), can be modeled using modular networks comprised of small, densely connected groups of nodes (Girvan & Newman, 2002). These modules often overlap, with network elements belonging to multiple modules (Palla et al. 2005; Ahn et al. 2010). Yet existing work on robustness has not considered the role of overlapping, modular structure. Here we study the robustness of these systems to the failure of elements. We show analytically and empirically that it is possible for the modules themselves to become uncoupled or non-overlapping well before the network disintegrates. If overlapping modular organization plays a role in overall functionality, networks may be far more vulnerable than predicted by conventional percolation theory.

In this paper, we develop a formal framework for what a good community should look like and how strong a community is (community strength). One of the key innovations is to incorporate the concept of relative centrality into structural analysis of networks. In our framework, relative centrality is a measure that measures how important a set of nodes in a network is with respect to another set of nodes, and it is a generalization of centrality. Building on top of relative centrality, the community strength for a set of nodes is measured by the difference between its relative centrality with respect to itself and its centrality. A community is then a set of nodes with a nonnegative community strength. We show that our community strength is related to conductance that is commonly used for measuring the strength of a small community. We define the modularity for a partition of a network as the average community strength for a randomly selected node. Such a definition generalizes the original Newman's modularity and recovers the stability in as special cases. For the local community detection problem, we also develop efficient agglomerative algorithms that guarantee the community strength of the detected local community.

Recent research indicates that knowledge about social networks can be leveraged to increase efficiency of interventions (Valente, 2012). However, in many settings, there exists considerable uncertainty regarding the structure of the network. This can render the estimation of potential effects of network-based interventions difficult, as providing appropriate guidance to select interventions often requires a representation of the whole network. In order to make use of the network property estimates to simulate the effect of interventions, it may be beneficial to sample networks from an estimated posterior predictive distribution, which can be specified using a wide range of models. Sampling networks from a posterior predictive distribution of network properties ensures that the uncertainty about network property parameters is adequately captured. The tendency for relationships among network properties to exhibit sharp thresholds has important implications for understanding global network topology in the presence of uncertainty; therefore, it is essential to account for uncertainty. We provide detail needed to sample networks for the specific network properties of degree distribution, mixing frequency, and clustering. Our methods to generate networks are demonstrated using simulated data and data from the National Longitudinal Study of Adolescent Health.

Face-to-face interactions in social groups are a central aspect of human social lives. Although the composition of such groups has received ample attention in various fields—e.g., sociology, social psychology, management, and educational science—their micro-level dynamics are rarely analyzed empirically. In this article, we present a new statistical network model (DyNAM-i) that can represent the dynamics of conversation groups and interpersonal interaction in different social contexts. Taking an actor-oriented perspective, this model can be applied to test how individuals’ interaction patterns differ and how they choose and change their interaction groups. It moves beyond dyadic interaction mechanisms and translates central social network mechanisms—such as homophily, transitivity, and popularity—to the context of interactions in group settings. The utility and practical applicability of the new model are illustrated in two social network studies that investigate face-to-face interactions in a small party and an office setting.

A measure of centrality is rank monotone if after adding an arc x → y, all nodes with a score smaller than (or equal to) y have still a score smaller than (or equal to) y. If, in particular, all nodes with a score smaller than or equal to y get a score smaller than y (i.e., all ties with y are broken in favor of y), the measure is called strictly rank monotone. We prove that harmonic centrality is strictly rank monotone, whereas closeness is just rank monotone on strongly connected graphs, and that some other measures, including betweenness, are not rank monotone at all (sometimes not even on strongly connected graphs). Among spectral measures, damped scores such as Katz's index and PageRank are strictly rank monotone on all graphs, whereas the dominant eigenvector is strictly monotone on strongly connected graphs only.

In this introduction to the special section on globalization, regionalization, and multi-polarity, we review network analysis applications to the study of globalization as a complex and multi-dimensional phenomenon and we explore the frontiers of our knowledge about the network properties of global systems. We focus on the global economic (trade and investment), political, and migration systems.

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.