Spectral Clustering with Epidemic Diffusion

TL;DR

This paper introduces a novel spectral clustering method based on epidemic diffusion, which emphasizes dense, clique-like communities by reweighting edges according to node centrality, outperforming traditional methods in certain structures.

Contribution

The paper proposes a new spectral clustering approach using epidemic diffusion properties, linking the replicator operator to the normalized Laplacian with centrality-based reweighting.

Findings

Replicator emphasizes dense, clique-like communities.

Method outperforms traditional spectral clustering on synthetic graphs.

Edges are reweighted by eigenvector centralities to improve community detection.

Abstract

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploits the properties of epidemic diffusion. An epidemic is a dynamic process that, unlike the random walk, simultaneously transitions to all the neighbors of a given node. We show that the replicator, an operator describing epidemic diffusion, is equivalent to the symmetric normalized Laplacian of a reweighted graph with edges reweighted by the eigenvector centralities of their incident nodes. Thus, more weight is given to edges connecting more central nodes. We describe a method that partitions the nodes based on the componentwise ratio of the replicator's second eigenvector to the first, and compare its performance to traditional spectral clustering techniques on synthetic graphs with known community structure. We demonstrate that the replicator gives preference to dense, clique-like structures, enabling it to more effectively discover communities that may be obscured by dense intercommunity linking.