Graver basis for an undirected graph and its application to testing the beta model of random graphs

TL;DR

This paper provides an explicit algorithmic description of the Graver basis for the toric ideal of a simple undirected graph and demonstrates its application in testing the beta model of random graphs using Markov chain Monte Carlo methods.

Contribution

It introduces a novel explicit and algorithmic characterization of the Graver basis for graph-related toric ideals and applies it to statistical testing of the beta model.

Findings

Explicit description of the Graver basis for undirected graphs

Application of the basis to beta model testing via MCMC

Enhanced understanding of graph-based statistical models

Abstract

In this paper we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method.