The link prediction task has found numerous applications in real-world scenarios. However, in most of the cases like interactions, purchases, mobility, etc., links can re-occur again and again across time. As a result, the data being generated is excessively large to handle, associated with the complexity and sparsity of networks. Therefore, we propose a very fast, memory-less, and dynamic sampling-based method for predicting recurring links for a successive future point in time. This method works by biasing the links exponentially based on their time of occurrence, frequency, and stability. To evaluate the efficiency of our method, we carried out rigorous experiments with massive real-world graph streams. Our empirical results show that the proposed method outperforms the state-of-the-art method for recurring links prediction. Additionally, we also empirically analyzed the evolution of links with the perspective of multi-graph topology and their recurrence probability over time.

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.

We assess the reliability of relational event model (REM) parameters estimated under two sampling schemes: (1) uniform sampling from the observed events and (2) case–control sampling which samples nonevents, or null dyads (“controls”), from a suitably defined risk set. We experimentally determine the variability of estimated parameters as a function of the number of sampled events and controls per event, respectively. Results suggest that REMs can be reliably fitted to networks with more than 12 million nodes connected by more than 360 million dyadic events by analyzing a sample of some tens of thousands of events and a small number of controls per event. Using the data that we collected on the Wikipedia editing network, we illustrate how network effects commonly included in empirical studies based on REMs need widely different sample sizes to be reliably estimated. For our analysis we use an open-source software which implements the two sampling schemes, allowing analysts to fit and analyze REMs to the same or other data that may be collected in different empirical settings, varying sample parameters or model specification.

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.

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.

In this paper, it is addressed how network structure can be related to asymptotic network behavior. If such a relation is studied, that usually concerns only strongly connected networks and only linear functions describing the dynamics. In this paper, both conditions are generalized. A couple of general theorems is presented that relates asymptotic behavior of a network to the network’s structure characteristics. The network structure characteristics, on the one hand, concern the network’s strongly connected components and their mutual connections; this generalizes the condition of being strongly connected to a very general condition. On the other hand, the network structure characteristics considered generalize from linear functions to functions that are normalized, monotonic, and scalar-free, so that many nonlinear functions are also covered. Thus, the contributed theorems generalize the existing theorems on the relation between network structure and asymptotic network behavior addressing only specific cases such as acyclic networks, fully, and strongly connected networks, and theorems addressing only linear functions. This paper was invited as an extended (by more than 45%) version of a Complex Networks’18 conference paper. In the discussion section, the differences are explained in more detail.

A person’s egonet, the set of others with whom that person is connected, is a personal sample of society which especially influences that person’s experience and perceptions of society. We show that egonets systematically misrepresent the general population because each person is included in as many egonets as that person has “friends.” Previous research has recognized that this unequal weighting in egonets leads many people to find that their friends have more friends than they themselves have. This paper builds upon that research to show that people’s egonets provide them with systematically biased samples of the population more generally. We discuss how this ubiquitous egonet bias may have far reaching implications for people’s experiences and perceptions of frequencies of other people’s ties and traits in ways that may influence their own feelings and behaviors. In particular, these egonet biases may help explain people’s tendencies to disproportionately experience and overestimate the prevalence of certain types of deviance and other social behaviors and consequently be influenced toward them. We illustrate egonet bias with analyses of all friends among 63,731 Facebook users. We call for further empirical investigation of egonet biases and their consequences for individuals and society.

We present a statistical framework for generating predicted dynamic networks based on the observed evolution of social relationships in a population. The framework includes a novel and flexible procedure to sample dynamic networks given a probability distribution on evolving network properties; it permits the use of a broad class of approaches to model trends, seasonal variability, uncertainty, and changes in population composition. Current methods do not account for the variability in the observed historical networks when predicting the network structure; the proposed method provides a principled approach to incorporate uncertainty in prediction. This advance aids in the designing of network-based interventions, as development of such interventions often requires prediction of the network structure in the presence and absence of the intervention. Two simulation studies are conducted to demonstrate the usefulness of generating predicted networks when designing network-based interventions. The framework is also illustrated by investigating results of potential interventions on bill passage rates using a dynamic network that represents the sponsor/co-sponsor relationships among senators derived from bills introduced in the U.S. Senate from 2003 to 2016.

When collecting egocentric network data, visual representations of networks can function as a cognitive aid for depicting relationships, helping to maintain an overview of the relationships, and keeping the attention of the interviewees. Additionally, network maps can serve as a narration generator in qualitative and in mixed-methods studies. While varying visual instruments are used for collecting egocentric network data, little is known about differences among visual tools concerning the influence on the resulting network data, the usability for interviewees, and data validity. The article provides an overview of existing visually oriented tools that are used to collect egocentric networks and discusses their functions, advantages, and limitations. Then, we present results of an experimental study where we compare four different visual tools with regard to networks elicited, manageability, and the impact of follow-up questions. In order to assess the manageability of the four tools, we used the thinking aloud method. The results provide evidence that the decision in favor of a specific visual tool (structured vs. unstructured) can affect the size and composition of the elicited networks. Follow-up questions greatly affect the elicited networks and follow-up cues can level out differences among tools. Respondents tend to prefer the concentric circles tool, with some differences in preferences and manageability of tools between participants with low and those with high socioeconomic status. Finally, assets and drawbacks of the four instruments are discussed with regard to data quality and crucial aspects of the data collection process when using visual tools.

We report on an interview method using photo-based network elicitation and a landmark anchoring event to collect data on relationship change in ego networks retrospectively. Using the wedding albums of married or formerly married respondents, we populate a network from many years ago with persons pictured in the album and then collect data about each respondent’s relationship with each person at the time of the wedding and at the time of the interview. This data collection method mitigates many of the problems associated with retrospective data collection and does not have the logistical difficulties associated with panel studies. Our findings show that this method is successful in collecting significant numbers of connections that have undergone change, and especially reductions in activity along various dimensions.

In network models for real-world domains, often network adaptation has to be addressed by incorporating certain network adaptation principles. In some cases, also higher order adaptation occurs: the adaptation principles themselves also change over time. To model such multilevel adaptation processes, it is useful to have some generic architecture. Such an architecture should describe and distinguish the dynamics within the network (base level), but also the dynamics of the network itself by certain adaptation principles (first-order adaptation level), and also the adaptation of these adaptation principles (second-order adaptation level), and may be still more levels of higher order adaptation. This paper introduces a multilevel network architecture for this, based on the notion network reification. Reification of a network occurs when a base network is extended by adding explicit states representing the characteristics of the structure of the base network. It will be shown how this construction can be used to explicitly represent network adaptation principles within a network. When the reified network is itself also reified, also second-order adaptation principles can be explicitly represented. The multilevel network reification construction introduced here is illustrated for an adaptive adaptation principle from social science for bonding based on homophily and one for metaplasticity in Cognitive Neuroscience.

We discuss a two-week summer course on “Network Science” and “Complex Systems” that we taught for 15 German high-school pupils of ages 16–18. In this course, we covered topics in graph theory, applied network science, programming, and dynamic systems alike. We find that “Network Science” is a well-suited course for introducing students to university-level mathematics. We reflect on difficulties regarding programming exercises and the discussion of more advanced topics in dynamic systems. We make the course material available and encourage fellow network scientists to organize similar outreach events.

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.

Bipartite networks represent pairwise relationships between nodes belonging to two distinct classes. While established methods exist for analyzing unipartite networks, those for bipartite network analysis are somewhat obscure and relatively less developed. Community detection in such instances is frequently approached by first projecting the network onto a unipartite network, a method where edges between node classes are encoded as edges within one class. Here we test seven different projection schemes by assessing the performance of community detection on both: (i) a real-world dataset from social media and (ii) an ensemble of artificial networks with prescribed community structure. A number of performance and accuracy issues become apparent from the experimental findings, especially in the case of long-tailed degree distributions. Of the methods tested, the “hyperbolic” projection scheme alleviates most of these difficulties and is thus the most robust scheme of those tested. We conclude that any interpretation of community detection algorithm performance on projected networks must be done with care as certain network configurations require strong community preference for the bipartite structure to be reflected in the unipartite communities. Our results have implications for the analysis of detected community structure in projected unipartite networks.

Who is more likely to be isolated from society in terms of political beliefs? To answer this question, we measure whether individuals’ beliefs are “out of sync”—the extent to which their views differ with their contemporaries—and examine how the level of synchronization is associated with the size of important-matter and political-matter discussion networks. The results show that people with weaker belief synchronization are more likely to have smaller important-matter discussion networks. However, additional analyses of political-matter discussion networks show that weaker belief synchronization is associated with smaller networks only among those without a high school diploma and even provides some advantage in maintaining larger networks for the college-educated. Overall, the results imply that political beliefs that are “out of sync” correspond to the individual being “out of society,” whereas the aspects of “out of society” are quite different among educational groups.

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.