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.

Domination and competition have been there since the beginning of the Universe. Bigger stars dominate the smaller ones and draw them towards themselves. Domination and competition are such phenomenon which nothing in this universe can stay without. Stronger things and animals dominate the weaker ones. Again, when there are more than one strong dominant, there comes competition among them. To measure domination and competition together, we introduce here a domination competition graph, through which we identify the most competitive and dominating variables. By dominating competition number, we calculate which nodes (when we draw a graph corresponding perception) are more powerful and how much powerful. We have used forest biodiversity network as an example here. In the end, an application of domination competitions to e-commerce industry is illustrated.