Counting spanning hypertrees in non-uniform hypergraphs based on sum operation

Abstract

The theoretical and applied research on hypergraph or hypernetwork is one of the hot topics of system science. Spanning hypertree extended from spanning tree is an interesting problem about this topic, but determining the number of spanning hypertrees in general hypergraphs is not suitable for generalizing from graph and more intractable. In this paper, we propose a definition of spanning hypertree which has less constraints than the traditional definition of spanning hypertree, and then find exact analytical expressions for the number of spanning hypertrees in several kinds of non-uniform hypergraphs based on sum operation. In addition, we define the entropy of spanning hypertree and conduct data experiments on the entropies of spanning hypertrees in four special classes of non-uniform hypergraphs.