Subhypergraphs in non-uniform random hypergraphs
- Tutte Institute for Mathematics and Computing
- Ryerson University
- Department of Applied Mathematics, Illinois Institute of Technology
- Tutte Institute for Mathematics and Computing
- Department of Mathematics, Ryerson University
- Department of Mathematics, University of Nebraska, Lincoln
- Tutte Institute for Mathematics and Computing
Abstract
In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable approach. We begin by defining a generalization of the binomial random graph model to hypergraphs and formalizing several definitions of subhypergraph. The bulk of the paper focusses on determining the expected existence of these types of subhypergraph in random hypergraphs. We also touch on the problem of determining whether a given subgraph appearing in the 2-section is likely to have been induced by a certain subhypergraph in the hypergraph. To evaluate the model in relation to real-world data, we compare model prediction to two datasets with respect to (1) the existence of certain small subhypergraphs, and (2) a clustering coefficient.