# Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models

## TL;DR

This paper introduces a spectral method for detecting low-dimensional structures in networks using arbitrary null models, effectively distinguishing meaningful communities from noise in both synthetic and real networks.

## Contribution

It presents a novel spectral estimation approach that utilizes generative models to identify significant network structures relative to any chosen null model.

## Key findings

- Effectively detects transitions between random and community structures in synthetic networks.
- Identifies noise nodes and community memberships accurately.
- Contrasts with traditional methods by showing null model choice impacts conclusions.

## Abstract

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network's low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network's eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.