A Mathematical Approach on Harmonic Centrality and Centralization of Some Graph Products

Abstract

In this paper, we derive the harmonic centrality of the vertices and the harmonic centralization of products of some important families of graphs. Centrality in graph theory and network analysis is based on the importance of a vertex in a graph. Our goal is to develop formulas that may be used to calculate the harmonic centrality and harmonic centralization of more complicated graphs. 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  with any of the path , cycle , star , and fan  graphs. For further studies, results can be derived for other families of graphs and other binary operations.