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.

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.

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.

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.

Latent stochastic blockmodels are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between nodes are observed at a number of different times. In this paper, we propose a new Bayesian framework to characterize the construction of connections. We rely on a Markovian property to describe the evolution of nodes' cluster memberships over time. We recast the problem of clustering the nodes of the network into a model-based context, showing that the integrated completed likelihood can be evaluated analytically for a number of likelihood models. Then, we propose a scalable greedy algorithm to maximize this quantity, thereby estimating both the optimal partition and the ideal number of groups in a single inferential framework. Finally, we propose applications of our methodology to both real and artificial datasets.

While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent work has made good advances (Almquist & Butts, 2014), but there is still the assumption that the dyads are conditionally independent given the edge histories. This assumption can be quite strong and is sometimes difficult to justify. If time steps are rather large, one would typically expect not only the existence of temporal dependencies among the dyads across observed time points but also the existence of simultaneous dependencies affecting how the dyads of the network co-evolve. We propose a general observation-driven model for dynamic networks that overcomes this problem by modeling both the mean and the covariance structures as functions of the edge histories using a flexible autoregressive approach. This approach can be shown to fit into a generalized linear mixed model framework. We propose a visualization method that provides evidence concerning the existence of simultaneous dependence. We describe a simulation study to determine the method's performance in the presence and absence of simultaneous dependence, and we analyze both a proximity network from conference attendees and a world trade network. We also use this last data set to illustrate how simultaneous dependencies become more prominent as the time intervals become coarser.

In dynamic networks, the presence of ties are subject both to endogenous network dependencies and spatial dependencies. Current statistical models for change over time are typically defined relative to some initial condition, thus skirting the issue of where the first network came from. Additionally, while these longitudinal network models may explain the dynamics of change in the network over time, they do not explain the change in those dynamics. We propose an extension to the longitudinal exponential random graph model that allows for simultaneous inference of the changes over time and the initial conditions, as well as relaxing assumptions of time-homogeneity. Estimation draws on recent Bayesian approaches for cross-sectional exponential random graph models and Bayesian hierarchical models. This is developed in the context of foreign direct investment relations in the global electricity industry in 1995–2003. International investment relations are known to be affected by factors related to: (i) the initial conditions determined by the geographical locations; (ii) time-dependent fluctuations in the global intensity of investment flows; and (iii) endogenous network dependencies. We rely on the well-known gravity model used in research on international trade to represent how spatial embedding and endogenous network dependencies jointly shape the dynamics of investment relations.

Dynamic network models describe many important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Until now, the literature has focused on static networks, which lack specific temporal interpretations.

We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links, and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We illustrate the flexibility of the method on both synthetic and real data.