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Phase transitions in a power-law uniform hypergraph

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  • Mingao Yuan

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.

Suggested Citation

  • Mingao Yuan, 2024. "Phase transitions in a power-law uniform hypergraph," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(4), pages 1257-1276, February.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:4:p:1257-1276
    DOI: 10.1080/03610926.2022.2097265
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