Alignment and integration of complex networks by hypergraph based spectral clustering
Complex networks possess a rich, multiscale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction, or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron Frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs. We illustrate our approach with applications for local and global alignment of protein protein interaction networks between multiple species, for tripartite community detection in folksonomies, and for detecting clusters of overlapping regulatory pathways in directed networks.
Physical review. E, Statistical, nonlinear, and soft matter physics