Phase transitions in a power-law uniform hypergraph

Mingao Yuan

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 4, 1257-1276

Abstract: We propose a power-law m-uniform random hypergraph on n vertices. In this hypergraph, each vertex is independently assigned a random weight from a power-law distribution with exponent α∈(0,∞). The hyperedge probabilities are defined as functions of the random weights. We characterize the number of hyperedges and the number of loose 2-cycles. There is a phase transition phenomenon for the number of hyperedges at α = 1. Interestingly, for the number of loose 2-cycles, phase transitions occur at both α = 1 and α = 2.

Date: 2024
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DOI: 10.1080/03610926.2022.2097265

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