Spectral Clustering with Epidemic Diffusion
This work addresses community detection in graphs, offering a novel approach that may enhance clustering in networks with complex linking patterns, though it appears incremental as it builds on existing spectral methods.
The authors tackled the problem of spectral clustering by proposing a new method based on epidemic diffusion, which reweights edges using eigenvector centralities to favor dense structures, and demonstrated improved performance in discovering communities obscured by dense interlinking on synthetic graphs.
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.