The concept of a network path has been foundational to network scholarship, enabling measures like betweenness, centrality, or reachability to capture how social actors connect and how information flows in a network. Advances in communication technology and the availability of fine grained time stamped interactions data necessitate rethinking the concept of network path to enable the development of measures, metrics and concepts uniquely adapted to capture the dynamics of social interactions. Building on the increasing recognition of the importance of microdynamics in social life, we advocate extending the notion of a network path into the temporal domain. We propose a framework for studying temporal structural dynamics in social networks, introducing metrics and measures tailored to capture the intricacies of ephemeral, time-sensitive relational processes. By integrating temporal dimensions, scholars can explore not only how and whether social actors connect, but also the temporal nuances of their interactions. This dynamic approach has profound theoretical implications for understanding relational processes and offers novel methodological tools for analyzing the evolving nature of human networks.

It is increasingly common to study mobility and migration of individuals between social and physical locations as networks in which locations are nodes connected by mobile individuals. This conceptualisation as mobility networks facilitates the analysis of how individuals influence one another in their mobility destinations.

Technically, this amounts to analysing interdependence between individuals' mobility paths. A recently proposed framework allows the statistical modelling of these social processes and, therefore, dependence in mobility, combining features of Exponential Random Graph Models (ERGMs) and classic log-linear models.

However, insufficient attention was paid to how such models should be specified in a principled, theoretically informed way. In this presentation, we apply statistical theory to propose model specifications that can be used to analyse emergent structures in mobility. In particular, we discuss how to specify models that (i) are based on clear dependence assumptions on the individual level, that (ii) have a clear individual level interpretation, that (iii) avoid (near-)degeneracy, a common problem for models with dependent observations, and (iv) that may be used to carry out population inference with sampled data.

Relational event models (REMs) describe temporal interactions between social actors, from the invasions of alien species, lending on the interbank market and patient transfers between hospitals. An important question in all of these, is what are the causal drivers underlying these processes. This is a causal discovery question and requires a causal inferential procedure that goes beyond MLE-based associative inference currently employed for REMs.

By exploiting the connection between REM partial likelihood under nested-case control sampling and logistic regression, we are able to use causal discovery methods recently developed for generalized linear models. In particular, we show that a causal relational event model is identified by means of two conditions: a standard MLE property and a crucial invariance property, expressed in terms of Pearson risk. The empirical analogue of these conditions requires a statistical test for the detection of the causal model among a set of candidate models. For this, we develop an efficient alternative to bootstrap, by deriving an approximate distribution of the standardized Pearson statistic under the causal model. We apply this method on a dataset of 350,000 events to investigate the causal drivers of bike sharing in Washington D.C.

Imagine a social network and most likely you will conjure up a picture of a static graph. In fact, this is how network models started to be developed by foundational work in the 1970s, followed in the 1980s by exponential random graph models. These models model the probability of the presence of an edge, possibly dependent on other edges. When temporal network data started to become available in the 1990s, an obvious choice was the temporal ERGM extension. Obvious, but not necessarily sensible. In fact, in the early 2000s SAOMs proposed modelling the presence of an edge not as a binary process, but as a temporal event history process. Pushing the connection with non-homogeneous Poisson process further, the relational event model (REM) introduced in 2008 has proven a particularly flexible model for modelling all kinds of relational processes, from alien species invasions, bike sharing, communication networks to lending on interbank markets.

In this talk I will sketch the most important developments in the history of dynamic network modelling, including TERGMS, SAOMs and Dynams, with a particular attention to relational event models. We describe the five-fold temporal dependence of relational events on time, and we show how new developments in REMs make the model ever more practical and adaptable to the needs of a practitioner.

Network data are widely collected across various domains, from biology to social sciences. The most common representation of these data is in the form of dyadic relationships, where pairs of nodes are connected by links. However, in some cases, groups of people are linked by higher-order interactions, such as two persons gossiping about a third one. Hypergraphs provide a framework for such interactions, where hyperedges represent subsets of nodes participating in the same event.

This work presents an extension of dynamic network models to higher-order interactions. By modeling hyper events via the proposed relational event model, we are able to analyze the temporal evolution of hyperedges and to uncover the dynamics of complex social phenomena. Using a rich dataset from a longitudinal study of over 40 secondary school communities in Hungary, we explore the dynamics of gossiping and the drivers underlying this social phenomenon. In this way, we are able to uncover patterns in how gossiping forms and evolves, offering new insights into social dynamics.

The new R-package MrQAP allows more flexible estimation of Multiple Regression Quadratic Assignment Procedure models in R. In this talk I will introduce the package, how to use it, and give some example applications on Cognitive Social Structure data. It is the first package that allows analyzing Cognitive Social Structures within a permutation regression framework, that is, network data where every participant not only reports about their ties but also about the ties they perceive others have. This forms a three dimensional data cube of senders, receivers, and perceivers, which can now be properly permuted.

The package comes with a variety of quality of life features: parallel processing, handling of many model families (OLS, logistic, Poisson, multinomial choice, etc.), heteroskedastic consistent estimators, random intercepts, within-group permutations, and handling of multiple networks at the same time. Naturally, the package is freely available on Github and hopefully soon on CRAN.

The statistical treatment of social network panel data often presupposes that micro-level network mechanisms generate observed macro-level outcomes, without fully accounting for the emergent meso-level network structures and the feedback mechanisms they may instantiate. To address this gap, we introduce a novel form of dependence in stochastic actor-oriented models (SAOMs), where actors’ network choices are influenced by their latent memberships in cohesive subgroups. These groups correspond to dense subgraphs in which actors are embedded and, as the network evolves over time, reflect shifting cohesive patterns. Formally, this is represented as the co-evolution of a one-mode network and a two-mode latent membership structure. The model requires prior ideas about the expected number of groups per actor and the number of actors per group, along with their variances. As application, we model school friendships, where cohesive subgroups represent unobserved peer groups formed among friends. We compare different specifications of friendship closure and find evidence that the social context of peer groups stabilizes and balances friendships, as students prefer to have more ties with their new groupmates. Furthermore, our results indicate that endogenous friendship dynamics induced by latent memberships better reproduces cohesive subgraphs observed at the network meso-level.

Exponential-family Random Graph Models (ERGMs) are vital for network analysis, yet parameter estimation remains challenging due to normalizing constant intractability. A popular approach, Stochastic Approximation (SA), works by repeatedly conducting a short simulation for the current parameter guess to obtain an estimate for the gradient of the log-likelihood, then making an update in the direction of the gradient whose magnitude is gradually reduced. A number of variants have been proposed, including Robbins-Monro and Equilibrium Expectations. Variants of SA are also found in machine learning, with the ADAptive Moments (ADAM) algorithm particularly popular for fitting neural network models. Each of these variants in turn involves further decisions such as how quickly the update size is reduced, and when the algorithm is determined to have converged.

We introduce a general framework that has these three variants as special cases. We conduct a series of simulation studies evaluating the impact of these settings on rate and reliability of convergence for difficult ERGM problems found in the literature. Through heuristic arguments and empirical study, we synthesise a variant of SA for ERGMs that seeks to draw on the best aspects of each of the existing.

For nearly two decades, Relational Event Models (REMs) have provided the framework for analyzing streams of time-stamped interactions. These models explain the governing dynamics of related relational phenomena based on statistics of previously observed events. However, as the size and complexity of temporal networks increase, REMs face computational bottlenecks. While several inference techniques have been proposed to reduce the computational costs of estimation procedures, improvements have been modest in optimizing the computation of history-based statistics.

We propose a series of estimators of explanatory statistics obtained from a sampled history of events. By deriving their theoretical properties, we can quantify and estimate their measurement errors, allowing us to make appropriate corrections during the estimation phase. Specifically, we fit REMs using error-in-variable techniques, including simulation-extrapolation methods. We assess the validity of our approach through both synthetic and real-world analyses designed to show the impact of history sampling and to compare our method to existing baseline techniques.

Our methodology enables the fitting of REMs to very large datasets, greatly expanding the practical applicability of these models.

This paper presents effects in Stochastic Actor-oriented Models for selection and influence in co-evolution of two two-mode networks with a common first node set which may be called 'actors'; the second node sets differ between the two networks; the first network serves to represent (by the one-mode projection) connections between the actors, who make choices of items in the second node set of the second network.

'Selection' refers to the impact of the item choices on the connections between actors in the first network, while 'influence' refers to the impact of the connections on the item choices in the second network.

Distinct specifications are proposed for selection and influence which are item-specific, and which refer to the number of items chosen (actor degrees in the second network). Descriptive statistics are proposed to represent the cross-sectional association between the two-mode networks, the explanation of which is the target of the selection and influence effects.

This is illustrated by an empirical example.

Devising the underlying generating mechanism of a real-life network is difficult as, more often than not, only its snapshots are available, but not its full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest form, results in a degree distribution that follows the power law. Consequently, the growth of real-life networks that roughly display such power-law behaviour is commonly modelled by preferential attachment. However, the validity of the power law has been challenged by the presence of alternatives with comparable performance, as well as the recent findings that the right tail of the degree distribution is often lighter than implied by the body, whilst still being heavy. In this paper, we study a modified version of the model with a flexible preference function that allows super/sub-linear behaviour whilst also guaranteeing that the limiting degree distribution has a heavy tail. We relate the distributions tail heaviness directly to the model parameters, allowing direct inference of the parameters from the degree distribution alone.

Co-voting networks provide important insights into political polarization, collaboration, and alliance formation in democratic systems. Here, we examine co-voting data from the United States Senate obtained from voteview.com, covering records from the 1st to the 119th Congress. Co-voting is represented in each Congress by a network in which senators are nodes, and two senators are adjacent if they voted together above a threshold rate. Such networks are structured both by shifts in the composition of the legislature, and by changing political forces that favor different types of alliance formation; these forces may vary over time in idiosyncratic ways, while also being consistent within particular periods (or even recurring to older patterns over time). This raises the challenge of modeling network behavior in a manner that is both flexible and well-regularized. Here, we employ a hierarchical Dirichlet process exponential family random graph mixture model (DP-ERGM) to infer the drivers of co-voting patterns across sessions. Our approach allows us to model hidden sub-populations of co-voting patterns over time, while using slab-and-spike priors to induce sparsity in the set of selected effects. We examine the incidence of drivers of voting patterns over time, apparent clustering in political forces generating voting behavior in different years, and the resulting graph distributions when marginalizing across latent subgroups. Implications for both voting patterns and the exploratory use of DP-ERGMs are discussed.

Citation networks are often used to quantify science, ranging from the impact of researchers, journals, or universities over to the interdisciplinarity or disruptiveness of papers. In this talk we present relational hyperevent models (RHEM) as a general modeling framework to assess patterns in the dynamics of citation networks. RHEM can be specified, among others, with endogenous effects (e.g., citing what many others cite or citing the work of those who previously cited the own work) and with random node-level effects representing the latent popularity of papers, or researchers. In an empirical analysis of more than 500,000 published papers we assess changes in one type of effects when controlling for others and estimate their relative explanatory power.

Stochastic actor-oriented models have been developed to analyze network dynamics when data are collected in a panel design. Several estimation methods are available, with the method of moments (MoM) being the default approach. This method is computed using a stochastic approximation algorithm, where the statistics that define the moment conditions naturally correspond to the parameters. Another approach is the generalized method of moments (GMoM), which extends MoM by incorporating more statistics than parameters. Although this method has been implemented and documented in Rsiena, guidelines on when to use the GMoM and which additional statistics to include are still lacking. In this paper, we present statistical approaches to determine when the additional statistics contribute useful information beyond what is provided by the moment conditions of the regular MoM. We also discuss the conditions under which the GMoM should be preferred over MoM.

The stochastic actor-oriented model (SAOM) represents change in network panel data as the outcome of actors' decision-making. The number of such decisions, therefore, serves as a natural operationalization of sample size. When there is a single dependent variable - whether a network or an actor attribute - this sample size is the primary determinant of the precision of estimates in SAOM-based data analyses and, consequently, of statistical power.

In co-evolution models, however, the situation becomes more complex. With multiple dependent variables, also sample size becomes multidimensional. Depending on the model specification, spillover effects between dependent variables may affect the precision of estimates. In this conference presentation, I propose a conceptual clarification and present empirically informed simulation studies that illustrate the main findings.