Harmonic Centrality and Centralization of Some Graph Products

TL;DR

This paper investigates harmonic centrality and centralization in graphs formed by Cartesian and direct products of paths, cycles, and fans, providing new insights into their structural importance measures.

Contribution

It presents novel results on harmonic centrality and centralization for specific graph products, expanding understanding of these measures in complex networks.

Findings

Derived formulas for harmonic centrality in product graphs

Analyzed how graph products affect centralization scores

Provided theoretical insights into network importance measures

Abstract

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.