Scalable motif-aware graph clustering

TL;DR

This paper introduces a scalable graph clustering approach based on motifs, especially triangles, which improves community detection by focusing on triangle conductance rather than traditional edge-based measures.

Contribution

It formalizes triangle conductance for graph clustering and extends existing techniques to incorporate motif-based signatures, demonstrating theoretical and empirical advantages.

Findings

Triangle conductance better captures community structure.

Motif-aware clustering outperforms traditional methods in experiments.

Theoretical results support the effectiveness of motif-based clustering.

Abstract

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our intuition, which has been suggested but not formalized similarly in previous works, is that triangles are a better signature of community than edges. We therefore generalize the notion of conductance for a graph to {\em triangle conductance}, where the edges are weighted according to the number of triangles containing the edge. This methodology allows us to develop variations of several existing clustering techniques, including spectral clustering, that minimize triangles split by the cluster instead of edges cut by the cluster. We provide theoretical results in a planted partition model to demonstrate the potential for triangle conductance in clustering problems. We then show experimentally the effectiveness of our methods to multiple applications in machine learning and graph mining.