Heat kernel based community detection

TL;DR

This paper introduces a deterministic local algorithm for heat kernel diffusion to detect communities in graphs, demonstrating improved community quality over PageRank with efficient computation.

Contribution

It presents the first deterministic, local algorithm for heat kernel diffusion and analyzes its localization and performance in community detection.

Findings

Heat kernel communities have better conductance than PageRank communities.

The algorithm is localized and runs in constant worst-case time depending on diffusion parameters.

Heat kernel communities outperform PageRank in real-world community detection tasks.

Abstract

The heat kernel is a particular type of graph diffusion that, like the much-used personalized PageRank diffusion, is useful in identifying a community nearby a starting seed node. We present the first deterministic, local algorithm to compute this diffusion and use that algorithm to study the communities that it produces. Our algorithm is formally a relaxation method for solving a linear system to estimate the matrix exponential in a degree-weighted norm. We prove that this algorithm stays localized in a large graph and has a worst-case constant runtime that depends only on the parameters of the diffusion, not the size of the graph. Our experiments on real-world networks indicate that the communities produced by this method have better conductance than those produced by PageRank, although they take slightly longer to compute on large graphs. On a real-world community identification task, the heat kernel communities perform better than those from the PageRank diffusion.