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arXiv · 2207.08542

Generations of random hypergraphs and random simplicial complexes by the map algebra

S. Ren
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Abstract

We consider the random hypergraph on a finite vertex set by choosing each set of vertices as an hyperedge independently at random. We express the probability distributions of the (lower-)associated simplicial complex and the (lower-)associated independence hypergraph of the random hypergraph in terms of the probability distributions of certain random simplicial complex and certain random independence hypergraph of Erd\"os-R\'enyi type. We construct a graded structure of the map algebra explicitly and give algorithms to generate random hypergraphs and random simplicial complexes.

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S. Ren. 2022-07-18. Generations of random hypergraphs and random simplicial complexes by the map algebra. https://arxiv.org/abs/2207.08542

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