# Spectral goodness of fit for network models

arXiv: https://arxiv.org/abs/1407.7247 · HTML: https://mlsanity.com/paper/1407.7247/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2014.

## Built on by (most cited first, 3 of 3)

- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Spectral goodness-of-fit tests for complete and partial network data](https://mlsanity.com/paper/2106.09702/) (2021)
- [Goodness-of-Fit of Attributed Probabilistic Graph Generative Models](https://mlsanity.com/paper/2308.03773/) (2023)

## Abstract (arXiv)

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.