Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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CLOSENESS CENTRALITY IN GRAPH PRODUCTS

Authors

  • R. G. Eballe
  • C. M. R. Balingit
  • I. S. Cabahug
  • A. L. V. Flores
  • S. M. B. Lumpayao
  • B. D. Peñalosa
  • G. A. L. Tampipi
  • C. A. Villarta

Keywords:

centrality, closeness centrality, graph products.

DOI:

https://doi.org/10.17654/0974165823034

Abstract

Closeness centrality is one of the three most widely known measures of centrality used in the analysis of social networks. It describes the relative importance of a particular vertex within a network or a graph by taking the average closeness of this vertex from all the others in that graph. In this paper, we present the closeness centrality of the vertices in four products of two graphs $G$ and $H$ such as their complete product $G \vee H$, corona product $G \circ H$, Cartesian product $G \square H$, and lexicographic product $G[H]$.

Received: February 14, 2023;
Revised: March 25, 2023;
Accepted: April 10, 2023;

References

S. P. Borgatti and M. G. Everett, A graph-theoretic perspective on centrality, Social Networks 28(4) (2006), 466-484.

F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, Redwood City, CA, 1990.

R. J. M. Damalerio, R. G. Eballe, C. M. R. Balingit, I. S. Cabahug Jr. and A. L. V. Flores, Global clustering coefficient of the join and corona of graphs, Asian Research Journal of Mathematics 18(12) (2022), 128-140. https://doi.org/10.9734/arjom/2022/v18i12632.

R. J. M. Damalerio and R. G. Eballe, Global clustering coefficient of the products of complete graphs, Asian Research Journal of Mathematics 18(6) (2022), 62-69. https://doi.org/10.9734/arjom/2022/v18i630384.

K. Das, S. Samanta and M. Pal, Study on centrality measures in social networks: a survey, Soc. Netw. Anal. Min. 13 (2018), 8. https://doi.org/10.1007/s13278-018-0493-2.

R. G. Eballe and I. S. Cabahug, Closeness centrality of some graph families, International Journal of Contemporary Mathematical Sciences 16(4) (2021), 127-134. doi:10.12988/ijcms.2021.91609.

F. Harary, Graph Theory, Addison-Wesley Publishing Company, Inc., USA, 1969.

S. Kumar, R. Unnithan, B. Kannan and M. Jathavedan, Betweenness centrality in some classes of graphs, International Journal of Combinatorics 2014 (2014), p. 12. https://doi.org/10.1155/2014/241723.

R. Sunil Kumar and Kannan Balakrishnan, Betweenness centrality in Cartesian product of graphs, AKCE Int. J. Graphs Comb. 17(1) (2020), 571-583.

Published

2023-05-11

Issue

Section

Articles

How to Cite

CLOSENESS CENTRALITY IN GRAPH PRODUCTS. (2023). Advances and Applications in Discrete Mathematics, 39(1), 29-41. https://doi.org/10.17654/0974165823034

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