# Network-ensemble comparisons with stochastic rewiring and von Neumann entropy

## TL;DR

This paper introduces a framework for comparing networks to random ensembles using stochastic rewiring and von Neumann entropy, providing a computationally efficient method to assess network typicality.

## Contribution

It develops a novel approach combining stochastic rewiring and von Neumann entropy to quantify network similarity to random ensembles without extensive simulations.

## Key findings

- Rewiring processes converge to Erdos-Renyi and configuration models.
- Von Neumann entropy effectively measures information content changes.
- Estimated rewiring steps needed for network to resemble ensemble.

## Abstract

Assessing whether a given network is typical or atypical for a random-network ensemble (i.e., network-ensemble comparison) has widespread applications ranging from null-model selection and hypothesis testing to clustering and classifying networks. We develop a framework for network-ensemble comparison by subjecting the network to stochastic rewiring. We study two rewiring processes, uniform and degree-preserved rewiring, which yield random-network ensembles that converge to the Erdos-Renyi and configuration-model ensembles, respectively. We study convergence through von Neumann entropy (VNE), a network summary statistic measuring information content based on the spectra of a Laplacian matrix, and develop a perturbation analysis for the expected effect of rewiring on VNE. Our analysis yields an estimate for how many rewires are required for a given network to resemble a typical network from an ensemble, offering a computationally efficient quantity for network-ensemble comparison that does not require simulation of the corresponding rewiring process.