Testing goodness-of-fit of random graph models

TL;DR

This paper develops goodness-of-fit tests for random graph models, including extensions of the Rasch and beta models, to assess how well these models fit observed network data.

Contribution

It introduces new goodness-of-fit testing methods for the Rasch, beta, and block models in random graph analysis.

Findings

Developed goodness-of-fit tests for the Rasch and beta models

Extended the models to include block structures

Provided methods to evaluate model fit with empirical data

Abstract

Random graphs are matrices with independent 0, 1 elements with probabilities determined by a small number of parameters. One of the oldest model is the Rasch model where the odds are ratios of positive numbers scaling the rows and columns. Later Persi Diaconis with his coworkers rediscovered the model for symmetric matrices and called the model beta. Here we give goodnes-of-fit tests for the model and extend the model to a version of the block model introduced by Holland, Laskey, and Leinhard.