# Inference for Network Regression Models with Community Structure

arXiv: https://arxiv.org/abs/2106.04271 · HTML: https://mlsanity.com/paper/2106.04271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 36 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 2 of 2)

- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)

## Built on by (most cited first, 1 of 1)

- [Covariate-assisted graph matching](https://mlsanity.com/paper/2512.11761/) (2025)

## Abstract (arXiv)

Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately modeling the residual dependencies among the relations. Frequently homogeneity assumptions are placed on the errors which are commonly incorrect and ignore critical, natural clustering of the actors. In this work, we present a novel regression modeling framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability properties of the error distribution to obtain parsimonious standard errors for regression parameters.