# Spectral goodness-of-fit tests for complete and partial network data

arXiv: https://arxiv.org/abs/2106.09702 · HTML: https://mlsanity.com/paper/2106.09702/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 13 of 13)

- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [A goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/1412.4857/) (2014)
- [Hypothesis Testing for Automated Community Detection in Networks](https://mlsanity.com/paper/1311.2694/) (2013)
- [Identifying the latent space geometry of network models through analysis of curvature](https://mlsanity.com/paper/2012.10559/) (2020)
- [Testing for Global Network Structure Using Small Subgraph Statistics](https://mlsanity.com/paper/1710.00862/) (2017)
- [Using Maximum Entry-Wise Deviation to Test the Goodness-of-Fit for Stochastic Block Models](https://mlsanity.com/paper/1703.06558/) (2017)
- [A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network](https://mlsanity.com/paper/1806.11220/) (2018)
- [Adjusted chi-square test for degree-corrected block models](https://mlsanity.com/paper/2012.15047/) (2020)
- [Spectral goodness of fit for network models](https://mlsanity.com/paper/1407.7247/) (2014)
- [Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels](https://mlsanity.com/paper/1612.06040/) (2016)
- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Using Aggregated Relational Data to feasibly identify network structure without network data](https://mlsanity.com/paper/1703.04157/) (2017)
- [Exponential Random Graph models for Little Networks](https://mlsanity.com/paper/1904.10406/) (2019)

## Abstract (arXiv)

Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well and will extrapolate to similar data. We use recent results in random matrix theory to derive a general goodness-of-fit test for dyadic data. We show that our method, when applied to a specific model of interest, provides an straightforward, computationally fast way of selecting parameters in a number of commonly used network models. For example, we show how to select the dimension of the latent space in latent space models. Unlike other network goodness-of-fit methods, our general approach does not require simulating from a candidate parametric model, which can be cumbersome with large graphs, and eliminates the need to choose a particular set of statistics on the graph for comparison. It also allows us to perform goodness-of-fit tests on partial network data, such as Aggregated Relational Data. We show with simulations that our method performs well in many situations of interest. We analyze several empirically relevant networks and show that our method leads to improved community detection algorithms. R code to implement our method is available on Github.