Asian Research Journal of Mathematics

Harmonic Centrality and Centralization of Some Graph Products

Jose Mari E. Ortega *

Mathematics Unit, Philippine Science High School Southern Mindanao Campus, Brgy. Sto. Nino, Davao City, Philippines.

Rolito G. Eballe

Mathematics Department, College of Arts and Sciences, Central Mindanao University, Musuan, Maramag, Bukidnon, Philippines.

*Author to whom correspondence should be addressed.

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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 P₂ with any of the path P_m, cycle C_m, and fan F_m graphs.

Keywords: Harmonic centrality, harmonic centralization, graph products

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