# Modeling Network Populations via Graph Distances

## TL;DR

This paper develops a probabilistic framework for modeling multiple networks using a Fréchet mean graph and a concentration parameter, enabling flexible distribution modeling and Bayesian inference, demonstrated through simulations and real data from biology and neuroscience.

## Contribution

Introduces a novel class of network models based on graph distances and Fréchet means, with a hierarchical Bayesian approach for inference.

## Key findings

- Effective modeling of network populations using the proposed framework.
- Successful application to biological and neuroscience data.
- Demonstrated flexibility and robustness through simulations.

## Abstract

This article introduces a new class of models for multiple networks. The core idea is to parametrize a distribution on labelled graphs in terms of a Fr\'{e}chet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fr\'{e}chet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience.