Is it always beneficial to create a new relationship (have a new follower/friend) in a social network? This question can be formally stated as a property of the centrality measure that defines the importance of the actors of the network. Score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target of the arc relatively to the remaining nodes. It is known that most centralities are both score and rank monotone on directed, strongly connected graphs. In this paper, we study the problem of score and rank monotonicity for classical centrality measures in the case of undirected networks: in this case, we require that score, or relative importance, improves at both endpoints of the new edge. We show that, surprisingly, the situation in the undirected case is very different, and in particular that closeness, harmonic centrality, betweenness, eigenvector centrality, Seeley’s index, Katz’s index, and PageRank are not rank monotone; betweenness and PageRank are not even score monotone. In other words, while it is always a good thing to get a new follower, it is not always beneficial to get a new friend.

Relational event models (REMs) for the analysis of social interaction were first introduced 15 years ago. Since then, a number of important substantive and methodological contributions have produced their progressive refinement and hence facilitated their increased adoption in studies of social and other networks. Today REMs represent a well-established class of statistical models for relational processes. This special issue of Network Science demonstrates the standing and recognition that REMs have achieved within the network analysis and networks science communities. We wrote this brief introductory editorial essay with four main objectives in mind: (i) positioning relational event data and models in the larger context of contemporary network science and social network research; (ii) reviewing some of the most important recent developments; (iii) presenting the innovative studies collected in this special issue as evidence of the empirical value of REMs, and (iv) identifying open questions and future research directions.

Polarization makes it difficult to form positive relationships across existing groups. Decreasing polarization may improve political discourse around the world. Polarization can be modeled on a social network as structural balance, where the network is composed of groups with positive links between all individuals in the group and negative links with all others. Previous work shows that incorporating attributes of individuals usually makes structural balance, and hence polarization, harder to achieve. That work examines only a limited number and types of attributes. We present a generalized model and a simulation framework to analyze the effect of any type of attribute, including analytically as long as an expected value can be written for the type of attribute. As attributes, we consider people’s (approximately) immutable characteristics (e.g., race, wealth) and such opinions that change more slowly than relationships (e.g., political preferences). We detail and analyze five classes of attributes, recapitulating the results of previous work in this framework and extending it. While it is easier to prevent than to destabilize polarization, we find that usually the most effective at both are continuous attributes, followed by ordered attributes and, finally, binary attributes. The effectiveness of unordered attributes varies depending on the magnitude of negative impact of having differing attributes but is smaller than of continuous ones. Testing the framework on network structures containing communities revealed that destroying polarization may require introducing local tensions. This model could be used by policymakers, among others, to prevent and design effective interventions to counteract polarization.

Multilayer networks are in the focus of the current complex network study. In such networks, multiple types of links may exist as well as many attributes for nodes. To fully use multilayer—and other types of complex networks in applications, the merging of various data with topological information renders a powerful analysis. First, we suggest a simple way of representing network data in a data matrix where rows correspond to the nodes and columns correspond to the data items. The number of columns is allowed to be arbitrary, so that the data matrix can be easily expanded by adding columns. The data matrix can be chosen according to targets of the analysis and may vary a lot from case to case. Next, we partition the rows of the data matrix into communities using a method which allows maximal compression of the data matrix. For compressing a data matrix, we suggest to extend so-called regular decomposition method for non-square matrices. We illustrate our method for several types of data matrices, in particular, distance matrices, and matrices obtained by augmenting a distance matrix by a column of node degrees, or by concatenating several distance matrices corresponding to layers of a multilayer network. We illustrate our method with synthetic power-law graphs and two real networks: an Internet autonomous systems graph and a world airline graph. We compare the outputs of different community recovery methods on these graphs and discuss how incorporating node degrees as a separate column to the data matrix leads our method to identify community structures well-aligned with tiered hierarchical structures commonly encountered in complex scale-free networks.

We create a framework to analyze the timing and frequency of instantaneous interactions between pairs of entities. This type of interaction data is especially common nowadays and easily available. Examples of instantaneous interactions include email networks, phone call networks, and some common types of technological and transportation networks. Our framework relies on a novel extension of the latent position network model: we assume that the entities are embedded in a latent Euclidean space and that they move along individual trajectories which are continuous over time. These trajectories are used to characterize the timing and frequency of the pairwise interactions. We discuss an inferential framework where we estimate the individual trajectories from the observed interaction data and propose applications on artificial and real data.

As relational event models are an increasingly popular model for studying relational structures, the reliability of large-scale event data collection becomes more and more important. Automated or human-coded events often suffer from non-negligible false-discovery rates in event identification. And most sensor data are primarily based on actors’ spatial proximity for predefined time windows; hence, the observed events could relate either to a social relationship or random co-location. Both examples imply spurious events that may bias estimates and inference. We propose the Relational Event Model for Spurious Events (REMSE), an extension to existing approaches for interaction data. The model provides a flexible solution for modeling data while controlling for spurious events. Estimation of our model is carried out in an empirical Bayesian approach via data augmentation. Based on a simulation study, we investigate the properties of the estimation procedure. To demonstrate its usefulness in two distinct applications, we employ this model to combat events from the Syrian civil war and student co-location data. Results from the simulation and the applications identify the REMSE as a suitable approach to modeling relational event data in the presence of spurious events.

We discuss a recently proposed family of statistical network models—relational hyperevent models (RHEMs)—for analyzing team selection and team performance in scientific coauthor networks. The underlying rationale for using RHEM in studies of coauthor networks is that scientific collaboration is intrinsically polyadic, that is, it typically involves teams of any size. Consequently, RHEM specify publication rates associated with hyperedges representing groups of scientists of any size. Going beyond previous work on RHEM for meeting data, we adapt this model family to settings in which relational hyperevents have a dedicated outcome, such as a scientific paper with a measurable impact (e.g., the received number of citations). Relational outcome can on the one hand be used to specify additional explanatory variables in RHEM since the probability of coauthoring may be influenced, for instance, by prior (shared) success of scientists. On the other hand, relational outcome can also serve as a response variable in models seeking to explain the performance of scientific teams. To tackle the latter, we propose relational hyperevent outcome models that are closely related with RHEM to the point that both model families can specify the likelihood of scientific collaboration—and the expected performance, respectively—with the same set of explanatory variables allowing to assess, for instance, whether variables leading to increased collaboration also tend to increase scientific impact. For illustration, we apply RHEM to empirical coauthor networks comprising more than 350,000 published papers by scientists working in three scientific disciplines. Our models explain scientific collaboration and impact by, among others, individual activity (preferential attachment), shared activity (familiarity), triadic closure, prior individual and shared success, and prior success disparity among the members of hyperedges.

Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.

Previous studies have shown that relationship sentiments in families follow a pattern wherein either all maintain positive relationships or there are two antagonistic factions. This result is consistent with the network theory of structural balance that individuals befriend their friends’ friend and become enemies with their friends’ enemies. Fault lines in families would then endogenously emerge through the same kinds of interactional processes that organize nations into axis and allies. We argue that observed patterns may instead exogenously come about as the result of personal characteristics or homophilous partitions of family members. Disentangling these alternate theoretical possibilities requires longitudinal data. The present study tracks the sentiment dynamics of 1,710 families in a longitudinal panel study. Results show the same static patterns suggestive of balancing processes identified in earlier research, yet dynamic analysis reveals that conflict in families is not generated or resolved in accordance with balance theory.

Despite the importance of diverse expertise in helping solve difficult interdisciplinary problems, measuring it is challenging and often relies on proxy measures and presumptive correlates of actual knowledge and experience. To address this challenge, we propose a text-based measure that uses researcher’s prior work to estimate their substantive expertise. These expertise estimates are then used to measure team-level expertise diversity by determining similarity or dissimilarity in members’ prior knowledge and skills. Using this measure on 2.8 million team invented patents granted by the US Patent Office, we show evidence of trends in expertise diversity over time and across team sizes, as well as its relationship with the quality and impact of a team’s innovation output.

The 2011 policy pivot of the German government, from extending nuclear power plants terms to securing their shutdown for 2022, cannot be explained without looking at how the German political discourse network shifted in the months following Fukushima. This paper seeks to model and identify mechanisms that help explain how the two-mode network of political actors’ support for claims developed. We identify possible mechanisms to explain discourse dynamics from literature on political discourse and discourse networks, and extend homophily mechanisms to two-mode networks as “tertius” effects. We then introduce and employ a multimodal extension of dynamic network actor models to answer two questions key to how the discourse has evolved: which actors support claims more frequently and which claims they support. Our results indicate that mechanisms vary according to the discursive phase, but that powerful actors participate in the discourse more often, and actors tend to support claims that have already found support by cross-party coalitions. These are the two most prominent mechanisms that help to explain the dramatic nuclear policy change in Germany after Fukushima.

In this paper, we examine the contribution of Network Science journal to the network science discipline. We do so from two perspectives. First, expanding the existing taxonomy of article contribution, we examine trends in theory testing, theory building, and new method development within the journal’s articles. We find that the journal demands a high level of theoretical contribution and methodological rigor. High levels of theoretical and methodological contribution become significant predictors of article citation rates. Second, we look at the composition of the studies in Network Science and determine that the journal has already established a solid “hard core” for the new discipline.

The global and uneven spread of COVID-19, mirrored at the local scale, reveals stark differences along racial and ethnic lines. We respond to the pressing need to understand these divergent outcomes via neighborhood level analysis of mobility and case count information. Using data from Chicago over 2020, we leverage a metapopulation Susceptible-Exposed-Infectious-Removed model to reconstruct and simulate the spread of SARS-CoV-2 at the ZIP Code level. We demonstrate that exposures are mostly contained within one’s own ZIP Code and demographic group. Building on this observation, we illustrate that we can understand epidemic progression using a composite metric combining the volume of mobility and the risk that each trip represents, while separately these factors fail to explain the observed heterogeneity in neighborhood level outcomes. Having established this result, we next uncover how group level differences in these factors give rise to disparities in case rates along racial and ethnic lines. Following this, we ask what-if questions to quantify how segregation impacts COVID-19 case rates via altering mobility patterns. We find that segregation in the mobility network has contributed to inequality in case rates across demographic groups.

David Gibson’s (2008) examination of research on conversational interaction highlighted methodological and theoretical gaps in current understanding – particularly around the localized construction of interaction and the reproduction of social structures. This paper extends extant formal models used by group process researchers to explain how exogenous status structures shape local interaction by incorporating insights from qualitative work examining the local production of conversational interaction. Relational events serve as a bridge between conversation analytic understandings of the deep structure of conversation and expectation states formal models of permeation. We propose a theoretical integration of the status organizing process (permeation) and local turn-taking rules (deep structure) as a more complete model of conversational behavior in task groups. We test a formalized construction of this preliminary theory by examining turn-taking using data from 55 task groups whose members vary in gender, authority, and legitimacy of that authority. This integrated model offers substantial improvements in prediction accuracy over using status information alone. We then propose ways to expand the integrated theoretical framework to advance current understandings of action and events in conversation. Finally, we offer suggestions for insights from group processes theories that could be incorporated into network models of interaction outside of this theoretical framework.

Finding paths is a fundamental problem in graph theory and algorithm design due to its many applications. Recently, this problem has been considered on temporal graphs, where edges may change over a discrete time domain. The analysis of graphs has also taken into account the relevance of vertex properties, modeled by assigning to vertices labels or colors. In this work, we deal with a problem that, given a static or temporal graph, whose vertices are colored graph looks for a path such that (1) the vertices of the path have distinct colors and (2) that path includes the maximum number of colors. We analyze the approximation complexity of the problem on static and temporal graphs, and we prove an inapproximability bound. Then, we consider the problem on temporal graphs, and we design a heuristic for it. We present an experimental evaluation of our heuristic, both on synthetic and real-world graphs. The experimental results show that for many instances of the problem, our method is able to return near-optimal solutions.

We study Granger Causality in the context of wide-sense stationary time series. The focus of the analysis is to understand how the underlying topological structure of the causality graph affects graph recovery by means of the pairwise testing heuristic. Our main theoretical result establishes a sufficient condition (in particular, the graph must satisfy a polytree assumption we refer to as strong causality) under which the graph can be recovered by means of unconditional and binary pairwise causality testing. Examples from the gene regulatory network literature are provided which establish that graphs which are strongly causal, or very nearly so, can be expected to arise in practice. We implement finite sample heuristics derived from our theory, and use simulation to compare our pairwise testing heuristic against LASSO-based methods. These simulations show that, for graphs which are strongly causal (or small perturbations thereof) the pairwise testing heuristic is able to more accurately recover the underlying graph. We show that the algorithm is scalable to graphs with thousands of nodes, and that, as long as structural assumptions are met, exhibits similar high-dimensional scaling properties as the LASSO. That is, performance degrades slowly while the system size increases and the number of available samples is held fixed. Finally, a proof-of-concept application example shows, by attempting to classify alcoholic individuals using only Granger causality graphs inferred from EEG measurements, that the inferred Granger causality graph topology carries identifiable features.

Dynamic Network Actor Models (DyNAMs) assume that an observed sequence of relational events is the outcome of an actor-oriented decision process consisting of two decision levels. The first level represents the time until an actor initiates the next relational event, modeled by an exponential distribution with an actor-specific activity rate. The second level describes the choice of the receiver of the event, modeled by a conditional multinomial logit model. The DyNAM assumes that the parameters are constant over the actors and the context. This homogeneity assumption, albeit statistically and computationally convenient, is difficult to justify, e.g., in the presence of unobserved differences between actors or contexts. In this paper, we extend DyNAMs by including random-effects parameters that vary across actors or contexts and allow controlling for unknown sources of heterogeneity. We illustrate the model by analyzing relational events among the users of an online community of aspiring and professional digital and graphic designers.

The social networks surrounding intimate couples provide them with bonding and bridging social capital and have been theorized to be associated with their well-being and relationship quality. These networks are multidimensional, featuring compositional (e.g., the proportion of family members vs. friends) and structural characteristics (e.g., density, degree of overlap between spouses’ networks). Most previous studies of couple networks are based on partners’ global ratings of their network characteristics or network data collected from one member of the dyad. This study presents the analysis of “duocentric networks" or the combined personal networks of both members of a couple, collected from 207 mixed-sex newlywed couples living in low-income neighborhoods of Harris County, TX. We conducted a pattern-centric analysis of compositional and structural features to identify distinct types of couple networks. We identified five qualitatively distinct network types (wife family-focused, husband family-focused, shared friends, wife friend-focused, and extremely disconnected). Couples’ network types were associated with the quality of the relationships between couples and their network contacts (e.g., emotional support) but not with the quality of the couples’ relationship with each other. We argue that duocentric networks provide appropriate data for measuring bonding and bridging capital in couple networks.

A stream of research on co-authorship, used as a proxy of scholars’ collaborative behavior, focuses on members of a given scientific community defined at discipline and/or national basis for which co-authorship data have to be retrieved. Recent literature pointed out that international digital libraries provide partial coverage of the entire scholar scientific production as well as under-coverage of the scholars in the community. Bias in retrieving co-authorship data of the community of interest can affect network construction and network measures in several ways, providing a partial picture of the real collaboration in writing papers among scholars. In this contribution, we collected bibliographic records of Italian academic statisticians from an online platform (IRIS) available at most universities. Even if it guarantees a high coverage rate of our population and its scientific production, it is necessary to deal with some data quality issues. Thus, a web scraping procedure based on a semi-automatic tool to retrieve publication metadata, as well as data management tools to detect duplicate records and to reconcile authors, is proposed. As a result of our procedure, it emerged that collaboration is an active and increasing practice for Italian academic statisticians with some differences according to the gender, the academic ranking, and the university location of scholars. The heuristic procedure to accomplish data quality issues in the IRIS platform can represent a working case report to adapt to other bibliographic archives with similar characteristics.