2023
DOI: 10.1088/1751-8121/accac0
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Random recursive hypergraphs

Abstract: Random recursive hypergraphs grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, and several characteristics of emerging hypergraphs admit neat expressions via harmonic numbers, Bernoulli numbers, Eulerian numbers, and Stirling numbers of the first kind. Natural deformations of random recursive hypergraphs give rise to fascinating models of growing random hypergraphs.

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Cited by 7 publications
(2 citation statements)
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“…When a > 0, the sum is estimated as in the a = 1 case presented after equation (52a). The asymptotic behaviors ( 65) and (66) indicate that the decay laws for the probability to have the maximal number of followers depend on whether the exponent larger or smaller than a = 0 corresponding to classical random maps. When a > 0, we obtain…”
Section: Fitness Modelsmentioning
confidence: 99%
See 1 more Smart Citation
“…When a > 0, the sum is estimated as in the a = 1 case presented after equation (52a). The asymptotic behaviors ( 65) and (66) indicate that the decay laws for the probability to have the maximal number of followers depend on whether the exponent larger or smaller than a = 0 corresponding to classical random maps. When a > 0, we obtain…”
Section: Fitness Modelsmentioning
confidence: 99%
“…These RRTs with an extra loop contain a single community and one egocentric, the founder, so they are less in the sociological realm than the RRM. A model of growing random hypergraphs known as random recursive hypergraphs [66] also overlaps with RRMs.…”
Section: Data Availability Statementmentioning
confidence: 99%