Magnetic eigenmaps for community detection in directed networks

摘要

Communities in directed networks have often been characterized as regions with a high density of links,or as sets of nodes with certain patterns of connection. Our approach for community detection combines theoptimization of a quality function and a spectral clustering of a deformation of the combinatorial Laplacian, theso-called magnetic Laplacian. The eigenfunctions of the magnetic Laplacian, which we call magnetic eigenmaps,incorporate structural information. Hence, using the magnetic eigenmaps, dense communities including directedcycles can be revealed as well as “role” communities in networks with a running flow, usually discoveredthanks to mixture models. Furthermore, in the spirit of the Markov stability method, an approach for studyingcommunities at different energy levels in the network is put forward, based on a quantum mechanical system atfinite temperature.