Abstract
We formally introduce in this paper two parameters in graph theory, namely, clique centrality and global clique centrality. Let G be a finite, simple and undirected graph of order n. A clique in G is a nonempty subset W \(\subseteq\) V (G) such that the subgraph \(\langle\)W\(\rangle\)G induced by W is complete. The maximum size of any clique containing vertex u \(\in\) V (G) is called the clique centrality of u in G. Normalizing the sum of the clique centralities of all the vertices of G will lead us to the global clique centrality of G, whose value ranges from \(\frac{1}{m}\) to 1. In this paper, we study some general properties of the global clique centrality and then evaluate it for some parameterized families of graphs.
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