Information-theoretic Limits for Community Detection in Network Models

TL;DR

This paper investigates the fundamental information-theoretic limits of community detection across various network models, identifying conditions under which node labels cannot be reliably recovered.

Contribution

It provides a comprehensive analysis of non-recoverability conditions for multiple network models, including static and dynamic versions, based on model parameters.

Findings

Non-recoverability depends on edge probabilities in SBM.

Latent space dimension and community spread affect recoverability.

Dynamic models have specific non-recoverability conditions.

Abstract

We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, the non-recoverability condition depends on the probabilities of having edges inside a community, and between different communities. For the Latent Space Model, the non-recoverability condition depends on the dimension of the latent space, and how far and spread are the communities in the latent space. For the Directed Preferential Attachment Model and the Directed Small-world Model, the non-recoverability condition depends on the ratio between homophily and neighborhood size. We also consider dynamic versions of the Stochastic Block Model and the Latent Space Model.