# Bayesian exponential random graph models for populations of networks

arXiv: https://arxiv.org/abs/2104.05110 · HTML: https://mlsanity.com/paper/2104.05110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generators](https://mlsanity.com/paper/2203.03673/) (2022)

## Abstract (arXiv)

The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging study collects one or more brain scans across multiple individuals, each of which can be modelled as a network with nodes corresponding to distinct brain regions and edges corresponding to structural or functional connections between these regions. Most statistical network models, however, were originally proposed to describe a single underlying relational structure, although recent years have seen a drive to extend these models to populations of networks. Here, we propose one such extension: a multilevel framework for populations of networks based on exponential random graph models. By pooling information across the individual networks, this framework provides a principled approach to characterise the relational structure for an entire population. To perform inference, we devise a novel exchange-within-Gibbs MCMC algorithm that generates samples from the doubly-intractable posterior. To illustrate our framework, we use it to assess group-level variations in networks derived from fMRI scans, enabling the inference of age-related differences in the topological structure of the brain's functional connectivity.