Complex networks possess a rich, multi-scale structure reflecting the dynamical and URLanization 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 such problems. Here we introduce a framework for multi-network analysis based on 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 tripartite community detection in folksonomies, for local and global alignment of protein-protein interaction networks between multiple species  and for detecting clusters of overlapping regulatory pathways in directed networks.
Complex networks possess a rich, multi-scale structure reflecting the dynamical and URLanization 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.
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such
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multi-network analysis based on
clustering and community detection in such systems using
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tripartite community detection in folksonomies, for
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, for tripartite community detection in folksonomies,