Enumeration of dihypergraphs with specified degrees and edge types

TL;DR

This paper derives asymptotic formulas for counting directed hypergraphs with specified degree sequences and hyperarc sizes, under certain size constraints.

Contribution

It provides the first known asymptotic enumeration formulas for dihypergraphs with given degrees and edge types.

Findings

Formulas hold when maximum degrees and sizes are not too large.

Applicable to hypergraphs modeling chemical reactions and relational databases.

Advances enumeration techniques for complex hypergraph structures.

Abstract

A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical reactions or relational databases. We provide asymptotic formulae for the number of directed hypergraphs with given in-degree sequence, out-degree sequence, and with the head and tail sizes of all hyperarcs specified. Our formulae hold when none of the following parameters are too large: the maximum out-degree, the maximum in-degree, the maximum head size and the maximum tail size.