2021/05/07 by Mingao Yuan, Yuan, Mingao
Computer Science · Physics and Astronomy · Mathematics · #Topological and Geometric Data Analysis #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2105.04296
We propose a power-law m-uniform random hypergraph on n vertexes. In this hypergraph, each vertex is independently assigned a random weight from a power-law distribution with exponent α∈(0,∞) and the hyperedge probabilities are defined as functions of the random weights. We characterize the number of hyperedge and the number of loose 2-cycle. There is a phase transition phenomenon for the number of hyperedge at α=1. Interestingly, for the number of loose 2-cycle, phase transition occurs at both α=1 and α=2.