Searching for a Single Community in a Graph

TL;DR

This paper introduces a method to efficiently find a specific community within a graph using side information, outperforming traditional clustering methods in accuracy and speed.

Contribution

It proposes a novel variant of the method of moments that leverages side information to target a single community more reliably and efficiently.

Findings

Significant improvements in runtime over existing algorithms.

Higher accuracy in identifying the target community.

Effective use of side information to enhance community detection.

Abstract

In standard graph clustering/community detection, one is interested in partitioning the graph into more densely connected subsets of nodes. In contrast, the "search" problem of this paper aims to only find the nodes in a "single" such community, the target, out of the many communities that may exist. To do so , we are given suitable side information about the target; for example, a very small number of nodes from the target are labeled as such. We consider a general yet simple notion of side information: all nodes are assumed to have random weights, with nodes in the target having higher weights on average. Given these weights and the graph, we develop a variant of the method of moments that identifies nodes in the target more reliably, and with lower computation, than generic community detection methods that do not use side information and partition the entire graph. Our empirical results show significant gains in runtime, and also gains in accuracy over other graph clustering algorithms.