Clique Centrality and Global Clique Centrality of Graphs

We formally introduce in this paper two parameters in graph theory, namely, clique centrality and globalclique centrality. LetGbe a finite, simple and undirected graph of ordern. A clique inGis a nonemptysubsetW⊆V(G) such that the subgraph〈W〉Ginduced byWis complete. The maximum size of anyclique containing vertexu∈V(G) is called the clique centrality ofuinG. Normalizing the sum of the cliquecentralities of all the vertices ofGwill lead us to the global clique centrality ofG, whose value ranges from1mto 1. In this paper, we study some general properties of the global clique centrality and then evaluate itfor some parameterized families of graphs.