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.

Exponential random graph models, or ERGMs, are a flexible and general class of models for modeling dependent data. While the early literature has shown them to be powerful in capturing many network features of interest, recent work highlights difficulties related to the models’ ill behavior, such as most of the probability mass being concentrated on a very small subset of the parameter space. This behavior limits both the applicability of an ERGM as a model for real data and inference and parameter estimation via the usual Markov chain Monte Carlo algorithms. To address this problem, we propose a new exponential family of models for random graphs that build on the standard ERGM framework. Specifically, we solve the problem of computational intractability and “degenerate” model behavior by an interpretable support restriction. We introduce a new parameter based on the graph-theoretic notion of degeneracy, a measure of sparsity whose value is commonly low in real-world networks. The new model family is supported on the sample space of graphs with bounded degeneracy and is called degeneracy-restricted ERGMs, or DERGMs for short. Since DERGMs generalize ERGMs—the latter is obtained from the former by setting the degeneracy parameter to be maximal—they inherit good theoretical properties, while at the same time place their mass more uniformly over realistic graphs. The support restriction allows the use of new (and fast) Monte Carlo methods for inference, thus making the models scalable and computationally tractable. We study various theoretical properties of DERGMs and illustrate how the support restriction improves the model behavior. We also present a fast Monte Carlo algorithm for parameter estimation that avoids many issues faced by Markov Chain Monte Carlo algorithms used for inference in ERGMs.

We review the empirical comparison of Stochastic Actor-oriented Models (SAOMs) and Temporal Exponential Random Graph Models (TERGMs) by Leifeld & Cranmer in this journal [Network Science 7(1):20–51, 2019]. When specifying their TERGM, they use exogenous nodal attributes calculated from the outcome networks’ observed degrees instead of endogenous ERGM equivalents of structural effects as used in the SAOM. This turns the modeled endogeneity into circularity and obtained results are tautological. In consequence, their out-of-sample predictions using TERGMs are based on out-of-sample information and thereby predict the future using observations from the future. Thus, their analysis rests on erroneous model specifications that invalidate the article’s conclusions. Finally, beyond these specific points, we argue that their evaluation metric—tie-level predictive accuracy—is unsuited for the task of comparing model performance.

The significance and influence of U.S. Supreme Court majority opinions derive in large part from opinions’ roles as precedents for future opinions. A growing body of literature seeks to understand what drives the use of opinions as precedents through the study of Supreme Court case citation patterns. We raise two limitations of existing work on Supreme Court citations. First, dyadic citations are typically aggregated to the case level before they are analyzed. Second, citations are treated as if they arise independently. We present a methodology for studying citations between Supreme Court opinions at the dyadic level, as a network, that overcomes these limitations. This methodology—the citation exponential random graph model, for which we provide user-friendly software—enables researchers to account for the effects of case characteristics and complex forms of network dependence in citation formation. We then analyze a network that includes all Supreme Court cases decided between 1950 and 2015. We find evidence for dependence processes, including reciprocity, transitivity, and popularity. The dependence effects are as substantively and statistically significant as the effects of exogenous covariates, indicating that models of Supreme Court citations should incorporate both the effects of case characteristics and the structure of past citations.

Centralities are a widely studied phenomenon in network science. In policy networks, central actors are of interest because they are assumed to control information flows, to link opposing coalitions and to directly impact decision-making. First, we study what type of actor (e.g., state authorities or interest groups) is able to occupy central positions in the highly institutionalized context of policy networks. Second, we then ask whether bonding or bridging centralities prove to be more stable over time. Third, we investigate how these types of centrality influence actors’ positions in a network over time. We therefore adopt a longitudinal perspective and run exponential random graph models, including lagged central network positions at t1 as the main independent variable for actors’ activity and popularity at t2. Results confirm that very few actors are able to maintain central positions over time.

The temporal exponential random graph model (TERGM) and the stochastic actor-oriented model (SAOM, e.g., SIENA) are popular models for longitudinal network analysis. We compare these models theoretically, via simulation, and through a real-data example in order to assess their relative strengths and weaknesses. Though we do not aim to make a general claim about either being superior to the other across all specifications, we highlight several theoretical differences the analyst might consider and find that with some specifications, the two models behave very similarly, while each model out-predicts the other one the more the specific assumptions of the respective model are met.

Social networks influence children and adolescents' physical activity. The focus of this paper is to examine the differences in the effects of physical activity on friendship selection, with eye to the implications on physical activity interventions for young children. Prior to implementing a network intervention in the field, it is important to understand potential heterogeneities in the effects that activity level have on network structure. In this study, the associations between activity level and cross-sectional network structure, and activity level and change in network structure are assessed. We studied a real-world friendship network among 81 children (average age 7.96 years) who lived in low SES neighborhoods, attended public schools, and attended one of two structured aftercare programs, of which one has existed and the other was new. We modeled network selection effects and cross-sectional properties, while accounting for potential heterogeneities between networks. There was heterogeneity in the effect of physical activity on both cross-sectional network structure and the formation and dissolution processes, both across time and between networks. This suggests that if peer selection processes are changing within a network, a static network intervention strategy for childhood physical activity could become inefficient as the network evolves.