Community detection in the sparse hypergraph stochastic block model

• Published in: Random structures & algorithms Vol. 59; no. 3; pp. 407 - 463
• Main Authors: Pal, Soumik, Zhu, Yizhe
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.10.2021; Wiley Subscription Services, Inc
• Subjects: Algorithms; community detection; Graph theory; Graphs; random tensor; self‐avoiding walk; sparse hypergraph; stochastic block model; Stochastic models
• ISSN: 1042-9832; 1098-2418
• DOI: 10.1002/rsa.21006

We consider the community detection problem in sparse random hypergraphs. Angelini et al. in [6] conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of two blocks: above the threshold, there is a spectral algorithm which asymptotically almost surely constructs a partition of the hypergraph correlated with the true partition. Our method is a generalization to random hypergraphs of the method developed by Massoulié (2014) for sparse random graphs.