Journal
PHYSICAL REVIEW E
Volume 86, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.86.056111
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Funding
- National Science Foundation [DMS-1009502]
- BBSRC [BBS/E/D/20211552] Funding Source: UKRI
- Biotechnology and Biological Sciences Research Council [BBS/E/D/20211552] Funding Source: researchfish
- Direct For Mathematical & Physical Scien [1009502] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1009502] Funding Source: National Science Foundation
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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.
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