Community detection in large hypergraphs

Abstract

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. Here, we propose a principled framework to model the organization of higher-order data. Our approach recovers community structure with accuracy exceeding that of currently available state-of-the-art algorithms, as tested in synthetic benchmarks with both hard and overlapping ground-truth partitions. Our model is flexible and allows capturing both assortative and disassortative community structures. Moreover, our method scales orders of magnitude faster than competing algorithms, making it suitable for the analysis of very large hypergraphs, containing millions of nodes and interactions among thousands of nodes. Our work constitutes a practical and general tool for hypergraph analysis, broadening our understanding of the organization of real-world higher-order systems.

Message-passing on hypergraphs: detectability, phase transitions and higher-order information

“…We focus on an extension to hypergraphs of the stochastic block model (SBM) [38,39], a generative model for networks with community structure. Several variants of the SBM [15], and of its mixed-membership version [16,17], have been extended to hypergraphs. The model we utilize is an extension of the dyadic SBM to hypergraphs and allows generalizing the seminal detectability results of Decelle et al [6,7] to higher-order interactions.…”

“…2 [17,41]. Our specific formulation of the likelihood is only one among many alternatives to model communities in hypergraphs.…”

“…Given the count X of hyperedges sampled from equation (17), we can sample the hyperedges. This operation is performed by independently sampling X times # a nodes from each community a.…”

“…However, many complex systems with interactions that extend beyond pairs are better modeled by hypergraphs [12], which generalize the simpler case of dyadic graphs. Phenomena that have been investigated on graphs are now readily explored on hypergraphs, with examples including diffusion processes, synchronization, phase transitions [13] and, more recently, community structure [14][15][16][17][18].…”

Community detection from fuzzy and higher-order perspectives

“…Hypergraphs are a generalization of traditional graphs that allow a hyperedge to connect any number of nodes, not just a pair of nodes. In hypergraphs, extracting communities can provide an accurate and nuanced understanding of complex systems characterized by non-paired higher-order interactions [54].…”