A New Hypernetwork Model Based on Matrix Operation

In this paper, we propose a new hypernetwork model based on Tracy-Singh Product on the correlation matrix of hypergraph. Node degree, node hyperdegree, and hyperedge degree and their corresponding polynomials are introduced to describe this hypernetwork model. It is shown that this kind of hypernetworks is fractal as its correlation matrix is a fractal matrix. The fractal parameter is then given. What´s more, this kind of hypernetworks is also small-world for the diameter won´t exceed twice the diameter of primitive hypergraph. By a novel product of node degree polynomial, node hyperdegree polynomial and hyperedge degree polynomial, node degree, node hyperdegree and hyperedge degree are obtained.