# A Class of Temporal Hierarchical Exponential Random Graph Models for Longitudinal Network Data

## TL;DR

This paper introduces a new class of statistical models called THERGM for analyzing longitudinal networks with community structure, capturing evolving clusters and network features over time.

## Contribution

It proposes a novel two-stage estimation strategy combining latent space clustering with temporal ERG models for dynamic network analysis.

## Key findings

- Effective in identifying evolving communities
- Good fit to simulated data
- Accurate link prediction results

## Abstract

As a representation of relational data over time series, longitudinal networks provide opportunities to study link formation processes. However, networks at scale often exhibits community structure (i.e. clustering), which may confound local structural effects if it is not considered appropriately in statistical analysis. To infer the (possibly) evolving clusters and other network structures (e.g. degree distribution and/or transitivity) within each community, simultaneously, we propose a class of statistical models named Temporal Hierarchical Exponential Random Graph Models (THERGM). Our generative model imposes a Markovian transition matrix for nodes to change their membership, and assumes they join new community in a preferential attachment way. For those remaining in the same cluster, they follow a specific temporal ERG model (TERGM). While a direct MCMC based Bayesian estimation is computational infeasible, we propose a two-stage strategy. At the first stage, a specific dynamic latent space model will be used as the working model for clustering. At the second stage, estimated memberships are taken as given to fit a TERG model in each cluster. We evaluate our methods on simulated data in terms of the mis-clustering rate, as well as the goodness of fit and link prediction accuracy.