  Complex networks possess a rich, multi-scale 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.
