Spectral goodness of fit for network models

TL;DR

The paper introduces the spectral goodness of fit (SGOF), a new statistic for evaluating how well network models explain observed network structures, offering an absolute fit measure similar to R-squared.

Contribution

It presents SGOF as a novel spectral-based statistic that compares diverse network models and provides an absolute measure of fit, filling gaps in existing methods.

Findings

SGOF effectively measures model fit for various network models.

Spectral approach offers a new way to compare models.

Illustrated with examples demonstrating its utility.

Abstract

We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure how well a network model explains the structure of an observed network. SGOF provides an absolute measure of fit, analogous to the standard R-squared in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.