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

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