Harmonic Centrality and Centralization of Some Graph Products
Asian Research Journal of Mathematics,
Page 42-51
DOI:
10.9734/arjom/2022/v18i530377
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 Pm, cycle Cm, and fan Fm graphs.
Keywords:
- Harmonic centrality
- harmonic centralization
- graph products
How to Cite
Ortega, J. M. E., & Eballe, R. G. (2022). Harmonic Centrality and Centralization of Some Graph Products. Asian Research Journal of Mathematics, 18(5), 42-51. https://doi.org/10.9734/arjom/2022/v18i530377
References
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Ortega JME, Eballe RG. Harmonic centrality of some graph families. Advances and Applications in Mathematical Sciences. 2022;21(5):2581-2598. Available:https://doi:10.5281/zenodo.6396942
Ortega JME, Eballe RG. Harmonic centralization of some graph families. Advances and Applications in Discrete Mathematics. 2022; 31:13-33. Available:https://doi:10.17654/0974165822023
Kumar S, Balakrishnan K. Betweenness centrality in Cartesian product of graphs. AKCE International Journal of Graphs and Combinatorics. 2020;17(1):571-583. Available:https://doi: 10.1016/j.akcej.2019.03.012
Balakrishnan R, Ranganathan K. A textbook of graph theory. 2nd Ed. Springer, New York; 2012.
Boldi P, Vigna S. Axioms for centrality. Internet Mathematics. 2014;10:222-262. Available:https://doi.org/10.1080/15427951.2013.865686.
Sanna C. On the p-adic valuation of harmonic numbers. Journal of Number Theory. 2016;166:4146. Available:https://doi:10.1016/j.jnt.2016.02.020
Gmez S. Centrality in networks: Finding the most important nodes. In: Moscato P., de Vries
N. (eds) Business and Consumer Analytics: New Ideas, Springer, Cham; 2019. Available:https://doi.org/10.1007/978-3-030-06222-4 8
Marchiori M, Latora V. Harmony in the small-world. Physica A: Statistical Mechanics and Its Applications. 2000;285(34):539546. Available:https://doi:10.1016/s0378-4371(00)00311-3
Dekker AH. Conceptual distance in social network analysis. Journal of Social Structure. 2005;6(3).
Rochat Y. Closeness centrality extended to unconnected graphs: The harmonic centrality index. Applications of Social Network Analysis (ASNA); 2009.
Ortega JME, Eballe RG. Harmonic centrality of some graph families. Advances and Applications in Mathematical Sciences. 2022;21(5):2581-2598. Available:https://doi:10.5281/zenodo.6396942
Ortega JME, Eballe RG. Harmonic centralization of some graph families. Advances and Applications in Discrete Mathematics. 2022; 31:13-33. Available:https://doi:10.17654/0974165822023
Kumar S, Balakrishnan K. Betweenness centrality in Cartesian product of graphs. AKCE International Journal of Graphs and Combinatorics. 2020;17(1):571-583. Available:https://doi: 10.1016/j.akcej.2019.03.012
Balakrishnan R, Ranganathan K. A textbook of graph theory. 2nd Ed. Springer, New York; 2012.
Boldi P, Vigna S. Axioms for centrality. Internet Mathematics. 2014;10:222-262. Available:https://doi.org/10.1080/15427951.2013.865686.
Sanna C. On the p-adic valuation of harmonic numbers. Journal of Number Theory. 2016;166:4146. Available:https://doi:10.1016/j.jnt.2016.02.020
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