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.

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.

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.

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.

This paper provides an examination of inter-organizational collaboration in the UK research system. Data are collected on organizational collaboration on projects funded by four key UK research councils: Arts and Humanities Research Council, Economic and Social Research Council, Engineering and Physical Sciences Research Council, and Biotechnology and Biological Sciences Research Council. The organizational partnerships include both academic and nonacademic institutions. A collaboration network is created for each research council, and an exponential random graph model is applied to inform on the mechanisms underpinning collaborative tie formation on research council-funded projects. We find that in the sciences, collaborative patterns are much more hierarchical and concentrated in a small handful of actors compared to the social sciences and humanities projects. Institutions that are members of the elite Russell Group (a set of 24 high-ranking UK universities) are much more likely to be involved in collaborations across research councils.

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes themselves. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representation of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we extend the framework for evaluating graph embeddings that was recently introduced in [15]. Now, the framework assigns two scores, local and global, to each embedding that measure the quality of an evaluated embedding for tasks that require good representation of local and, respectively, global properties of the network. The best embedding, if needed, can be selected in an unsupervised way, or the framework can identify a few embeddings that are worth further investigation. The framework is flexible and scalable and can deal with undirected/directed and weighted/unweighted graphs.

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.

While we know that adolescents tend to befriend peers who share their race and gender, it is unclear whether patterns of homophily vary according to the strength, intimacy, or connectedness of these relationships. By applying valued exponential random graph models to a sample of 153 adolescent friendship networks, I test whether tendencies towards same-race and same-gender friendships differ for strong versus weak relational ties. In nondiverse, primarily white networks, weak ties are more likely to connect same-race peers, while racial homophily is not associated with the formation of stronger friendships. As racial diversity increases, however, strong ties become more likely to connect same-race peers, while weaker bonds are less apt to be defined by racial homophily. Gender homophily defines the patterns of all friendship ties, but these tendencies are more pronounced for weaker connections. My results highlight the empirical value of considering tie strength when examining social processes in adolescent networks.

Researchers have found that although external attacks, exogenous shocks, and node knockouts can disrupt networked systems, they rarely lead to the system’s collapse. Although these processes are widely understood, most studies of how exogenous shocks affect networks rely on simulated or observational data. Thus, little is known about how groups of real individuals respond to external attacks. In this article, we employ an experimental design in which exogenous shocks, in the form of the unexpected removal of a teammate, are imposed on small teams of people who know each other. This allows us to causally identify the removed individual’s contribution to the team structure, the effect that an individual had on those they were connected, and the effect of the node knockout on the team. At the team level, we find that node knockouts decrease overall internal team communication. At the individual level, we find that node knockouts cause the remaining influential players to become more influential, while the remaining peripheral players become more isolated within their team. In addition, we also find that node knockouts may have a nominal influence on team performance. These findings shed light on how teams respond and adapt to node knockouts.

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.

We consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm.

Machine learning applications on large-scale network-structured data commonly encode network information in the form of node embeddings. Network embedding algorithms map the nodes into a low-dimensional space such that the nodes that are “similar” with respect to network topology are also close to each other in the embedding space. Real-world networks often have multiple versions or can be “multiplex” with multiple types of edges with different semantics. For such networks, computation of Consensus Embeddings based on the node embeddings of individual versions can be useful for various reasons, including privacy, efficiency, and effectiveness of analyses. Here, we systematically investigate the performance of three dimensionality reduction methods in computing consensus embeddings on networks with multiple versions: singular value decomposition, variational auto-encoders, and canonical correlation analysis (CCA). Our results show that (i) CCA outperforms other dimensionality reduction methods in computing concensus embeddings, (ii) in the context of link prediction, consensus embeddings can be used to make predictions with accuracy close to that provided by embeddings of integrated networks, and (iii) consensus embeddings can be used to improve the efficiency of combinatorial link prediction queries on multiple networks by multiple orders of magnitude.

Several papers have highlighted the potential of network science to appeal to a younger audience of high school children and provided lesson material on network science for high school children. However, network science also provides a great topic for outreach activities for primary school children. Therefore, this article gives a short summary of an outreach activity on network science for primary school children aged 8–12 years. The material provided in this article contains presentation material for a lesson of approximately 1 hour, including experiments, exercises, and quizzes, which can be used by other scientists interested in popularizing network science. We then discuss the lessons learned from this material.

For interventions that affect how individuals interact, social network data may aid in understanding the mechanisms through which an intervention is effective. Social networks may even be an intermediate outcome observed prior to end of the study. In fact, social networks may also mediate the effects of the intervention on the outcome of interest, and Sweet (2019) introduced a statistical model for social networks as mediators in network-level interventions. We build on their approach and introduce a new model in which the network is a mediator using a latent space approach. We investigate our model through a simulation study and a real-world analysis of teacher advice-seeking networks.

This study considers a network formation model in which each dyad of agents strategically determines the link status. Our model allows the agents to have unobserved group heterogeneity in the propensity of link formation. For the model estimation, we propose a three-step maximum likelihood method, in which the latent group structure is estimated using the binary segmentation algorithm in the second step. As an empirical illustration, we focus on the network data of international visa-free travels. The results indicate the presence of significant strategic complementarity and a certain level of degree heterogeneity in the network formation behavior.

In urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Our models successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.

Antisocial behavior can be contagious, spreading from individual to individual and rippling through social networks. Moreover, it can spread not only through third-party influence from observation, just like innovations or individual behavior do, but also through direct experience, via “pay-it-forward” retaliation. Here, we distinguish between the effects of observation and victimization for the contagion of antisocial behavior by analyzing large-scale digital trace data. We study the spread of cheating in more than a million matches of an online multiplayer first-person shooter game, in which up to 100 players compete individually or in teams against strangers. We identify event sequences in which a player who observes or is killed by a certain number of cheaters starts cheating and evaluate the extent to which these sequences would appear if we preserve the team and interaction structure but assume alternative gameplay scenarios. The results reveal that social contagion is only likely to exist for those who both observe and experience cheating, suggesting that third-party influence and “pay-it-forward” reciprocity interact positively. In addition, the effect is present only for those who both observe and experience more than once, suggesting that cheating is more likely to spread after repeated or multi-source exposure. Approaching online games as models of social systems, we use the findings to discuss strategies for targeted interventions to stem the spread of cheating and antisocial behavior more generally in online communities, schools, organizations, and sports.

Many real-world networks, including social networks and computer networks for example, are temporal networks. This means that the vertices and edges change over time. However, most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion of time. In this paper, we therefore introduce a generalized notion of discrete time for modeling temporal networks. Our approach also allows for considering nondeterministic time and incomplete data, two issues that are often found when analyzing datasets extracted from online social networks, for example. In order to demonstrate the consequences of our generalized notion of time, we also discuss the implications for the computation of (shortest) temporal paths in temporal networks. In addition, we implemented an R-package that provides programming support for all concepts discussed in this paper. The R-package is publicly available for download.

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.