Community Detection with and without Prior Information

TL;DR

This paper investigates how prior information about node clusters in sparse networks enhances community detection, showing that even minimal prior knowledge significantly lowers detection thresholds and improves community identification.

Contribution

It demonstrates that small amounts of prior information drastically improve community detection thresholds in sparse graphs, extending to weighted graphs for meaningful community definitions.

Findings

Prior knowledge reduces detection thresholds to their lowest possible value.

Even minimal prior information significantly improves community detection.

Weighted graphs allow for non-trivial community detection with semi-supervision.

Abstract

We study the problem of graph partitioning, or clustering, in sparse networks with prior information about the clusters. Specifically, we assume that for a fraction $\rho$ of the nodes their true cluster assignments are known in advance. This can be understood as a semi--supervised version of clustering, in contrast to unsupervised clustering where the only available information is the graph structure. In the unsupervised case, it is known that there is a threshold of the inter--cluster connectivity beyond which clusters cannot be detected. Here we study the impact of the prior information on the detection threshold, and show that even minute [but generic] values of $\rho>0$ shift the threshold downwards to its lowest possible value. For weighted graphs we show that a small semi--supervising can be used for a non-trivial definition of communities.