A study of cluster hypergraphs and its properties

Abstract

In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Few related terms and properties on cluster hypergraphs are discussed. Some operations, including the Cartesian product, union, intersection, etc., are studied. Different types of matrix representations and isomorphism are also proposed on cluster hypergraphs. The notion of an effective degree for nodes is introduced to capture the group/ cluster effects. At last, the area of applications and future directions with conclusions is deployed.