Alignment and integration of complex networks by hypergraph-based spectral clustering

TL;DR

This paper introduces a hypergraph-based spectral clustering framework for analyzing complex networks with multi-scale, multi-type interactions, enabling advanced community detection and network alignment beyond traditional pairwise methods.

Contribution

It generalizes the Perron-Frobenius theorem to hypergraphs and develops spectral clustering algorithms for directed and undirected systems, addressing a key gap in network analysis.

Findings

Effective clustering of protein-protein interaction networks across species

Detection of tripartite communities in folksonomies

Identification of overlapping regulatory pathway clusters

Abstract

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.