Phase transitions in a power-law uniform hypergraph
Mingao Yuan · Communication in Statistics- Theory and Methods · 2022
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.