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Harmonic centrality calculates the importance of a node in a network by adding the inverse of the geodesic distances of this node to all the other nodes. Harmonic centralization, on the other hand, is the graph-level centrality score based on the node-level harmonic centrality. In this paper, we present some results on both the harmonic centrality and harmonic centralization of graphs resulting from some graph products such as Cartesian and direct products of the path $P_2$ with any of the path $P_m$, cycle $C_m$, and fan $F_m$ graphs., Comment: 10 pages, 3 figures

Clustering coefficient is one of the most useful indices in complex networks. However, graph theoretic properties of this metric have not been discussed much in the literature, especially in graphs resulting from some binary operations. In this paper we present some expressions for the clustering coefficient of the tensor product of arbitrary graphs, regular graphs, and strongly regular graphs. A Vizing-type upperbound and a sharp lower bound for the clustering coefficient of the tensor product of graphs are also given., Comment: 9 pages, 1 figure, submitted to Advances and Applications in Mathematical Sciences (ISSN 0974-6803), corrected a typo error

One of the more recent measures of centrality in social network analysis is the normalized harmonic centrality. A variant of the closeness centrality, harmonic centrality sums the inverse of the geodesic distances of each node to other nodes where it is 0 if there is no path from one node to another. It is then normalized by dividing it by m-1, where m is the number of nodes of the graph. In this paper, we present notions regarding the harmonic centrality of some important classes of graphs., Comment: 13 pages, 5 figures