Community Detection: Exact Recovery in Weighted Graphs

TL;DR

This paper investigates the conditions for exact community recovery in weighted graphs with Gaussian or exponential edge distributions, providing tight criteria and extending analysis to incomplete graphs.

Contribution

It introduces a new semi-metric for weighted graphs that characterizes exact recovery conditions, extending previous models beyond Bernoulli edges.

Findings

Derived necessary and sufficient conditions for exact recovery

Introduced a semi-metric for weighted community detection

Extended analysis to incomplete weighted graphs

Abstract

In community detection, the exact recovery of communities (clusters) has been mainly investigated under the general stochastic block model with edges drawn from Bernoulli distributions. This paper considers the exact recovery of communities in a complete graph in which the graph edges are drawn from either a set of Gaussian distributions with community-dependent means and variances, or a set of exponential distributions with community-dependent means. For each case, we introduce a new semi-metric that describes sufficient and necessary conditions of exact recovery. The necessary and sufficient conditions are asymptotically tight. The analysis is also extended to incomplete, fully connected weighted graphs.