Fanuel Michaël, Alaíz Carlos M, Suykens Johan A K
Department of Electrical Engineering (ESAT) and STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium.
Phys Rev E. 2017 Feb;95(2-1):022302. doi: 10.1103/PhysRevE.95.022302. Epub 2017 Feb 8.
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 the optimization of a quality function and a spectral clustering of a deformation of the combinatorial Laplacian, the so-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 directed cycles can be revealed as well as "role" communities in networks with a running flow, usually discovered thanks to mixture models. Furthermore, in the spirit of the Markov stability method, an approach for studying communities at different energy levels in the network is put forward, based on a quantum mechanical system at finite temperature.
