Exact Recovery in the Geometric SBM

TL;DR

This paper characterizes the precise conditions under which exact community detection is possible in the Geometric Stochastic Block Model, a spatially-embedded network model inspired by social network transitivity.

Contribution

It provides a complete characterization of the information-theoretic threshold for exact recovery in the GSBM, extending previous results to a more general setting.

Findings

Derived the exact threshold for community recovery in GSBM

Generalized earlier results to broader conditions

Established theoretical limits for spatial community detection

Abstract

Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which inherently produce graphs containing many triangles. In this paper, we consider the problem of exact label recovery in the Geometric Stochastic Block Model (GSBM), a model proposed by Baccelli and Sankararaman as the spatially-embedded analogue of the well-studied Stochastic Block Model. Under mild technical assumptions, we completely characterize the information-theoretic threshold for exact recovery, generalizing the earlier work of Gaudio, Niu, and Wei.