# Modeling Network Populations via Graph Distances

arXiv: https://arxiv.org/abs/1904.07367 · HTML: https://mlsanity.com/paper/1904.07367/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2019.

## Built on by (most cited first, 13 of 13)

- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Multiscale Graph Comparison via the Embedded Laplacian Discrepancy](https://mlsanity.com/paper/2201.12064/) (2022)
- [Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral information](https://mlsanity.com/paper/2201.05923/) (2022)
- [On the Number of Edges of the Frechet Mean and Median Graphs](https://mlsanity.com/paper/2105.14397/) (2021)
- [Differentially Describing Groups of Graphs](https://mlsanity.com/paper/2201.04064/) (2021)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [When does the mean network capture the topology of a sample of networks?](https://mlsanity.com/paper/2408.03461/) (2024)
- [Approximate Fr'echet Mean for Data Sets of Sparse Graphs](https://mlsanity.com/paper/2105.04062/) (2021)
- [Sharp Threshold for the Frechet Mean (or Median) of Inhomogeneous Erdos-Renyi Random Graphs](https://mlsanity.com/paper/2201.11954/) (2022)
- [Probability density estimation for sets of large graphs with respect to spectral information using stochastic block models](https://mlsanity.com/paper/2207.02168/) (2022)
- [Estimation of the Sample Frechet Mean: A Convolutional Neural Network Approach](https://mlsanity.com/paper/2210.07401/) (2022)
- [The Spectral Barycentre of a Set of Graphs with Community Structure](https://mlsanity.com/paper/2502.00038/) (2025)
- [Metric space valued Fr'echet regression](https://mlsanity.com/paper/2602.05225/) (2026)

## Abstract (arXiv)

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'echet 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'echet 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.