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Betweenness centrality in convex amalgamation of graphs

Year 2019, Volume: 6 Issue: 1, 21 - 38, 19.01.2019
https://doi.org/10.13069/jacodesmath.508983

Abstract

Betweenness centrality measures the potential or power of a node to control the communication
over the network under the assumption that information flows primarily over the shortest
paths between pair of nodes. The removal of a node with highest betweenness from the network
will most disrupt communications between other nodes because it lies on the largest number
of paths. A large network can be thought of as inter-connection between smaller networks by
means of different graph operations. Thus the structure of a composite graph can be studied by
analysing its component graphs. In this paper we present the betweenness centrality of some
classes of composite graphs constructed by the graph operation called amalgamation or merging.

References

  • [1] A. Bavelas, A mathematical model for group structures, Human Organization 7, Appl. Anthropol. 7(3) (1948) 16–30.
  • [2] U. Brandes, A faster algorithm for betweenness centrality, J. Math. Sociol. 25(2) (2001) 163–177.
  • [3] L. C. Freeman, A set of measures of centrality based on betweenness, Sociometry 40(1) (1977) 35–41.
  • [4] R. Frucht, F. Haray, On the corona of two graphs, Aequationes Math. 4(3) (1970) 322–325.
  • [5] J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2009) 1–219.
  • [6] F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78(2) (1955) 445–463.
  • [7] S. Kumar, K. Balakrishnan, M. Jathavedan, Betweenness centrality in some classes of graphs, Int. J. Comb. 2014 (2014) 1–12.
  • [8] S. Kumar, K. Balakrishnan, On the number of geodesics of Petersen graph $ GP (n, 2)$, Electronic Notes in Discrete Mathematics 63 (2017) 295–302.
  • [9] S.-C. Shee, Y.-S. Ho, The cordiality of one-point union of n copies of a graph, Discrete Math. 117(1–3) (1993) 225–243.
Year 2019, Volume: 6 Issue: 1, 21 - 38, 19.01.2019
https://doi.org/10.13069/jacodesmath.508983

Abstract

References

  • [1] A. Bavelas, A mathematical model for group structures, Human Organization 7, Appl. Anthropol. 7(3) (1948) 16–30.
  • [2] U. Brandes, A faster algorithm for betweenness centrality, J. Math. Sociol. 25(2) (2001) 163–177.
  • [3] L. C. Freeman, A set of measures of centrality based on betweenness, Sociometry 40(1) (1977) 35–41.
  • [4] R. Frucht, F. Haray, On the corona of two graphs, Aequationes Math. 4(3) (1970) 322–325.
  • [5] J. A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2009) 1–219.
  • [6] F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78(2) (1955) 445–463.
  • [7] S. Kumar, K. Balakrishnan, M. Jathavedan, Betweenness centrality in some classes of graphs, Int. J. Comb. 2014 (2014) 1–12.
  • [8] S. Kumar, K. Balakrishnan, On the number of geodesics of Petersen graph $ GP (n, 2)$, Electronic Notes in Discrete Mathematics 63 (2017) 295–302.
  • [9] S.-C. Shee, Y.-S. Ho, The cordiality of one-point union of n copies of a graph, Discrete Math. 117(1–3) (1993) 225–243.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sunil Kumar Raghavan Unnithan 0000-0002-8254-6511

Kannan Balakrishnan This is me

Publication Date January 19, 2019
Published in Issue Year 2019 Volume: 6 Issue: 1

Cite

APA Kumar Raghavan Unnithan, S., & Balakrishnan, K. (2019). Betweenness centrality in convex amalgamation of graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, 6(1), 21-38. https://doi.org/10.13069/jacodesmath.508983
AMA Kumar Raghavan Unnithan S, Balakrishnan K. Betweenness centrality in convex amalgamation of graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. January 2019;6(1):21-38. doi:10.13069/jacodesmath.508983
Chicago Kumar Raghavan Unnithan, Sunil, and Kannan Balakrishnan. “Betweenness Centrality in Convex Amalgamation of Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 6, no. 1 (January 2019): 21-38. https://doi.org/10.13069/jacodesmath.508983.
EndNote Kumar Raghavan Unnithan S, Balakrishnan K (January 1, 2019) Betweenness centrality in convex amalgamation of graphs. Journal of Algebra Combinatorics Discrete Structures and Applications 6 1 21–38.
IEEE S. Kumar Raghavan Unnithan and K. Balakrishnan, “Betweenness centrality in convex amalgamation of graphs”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 1, pp. 21–38, 2019, doi: 10.13069/jacodesmath.508983.
ISNAD Kumar Raghavan Unnithan, Sunil - Balakrishnan, Kannan. “Betweenness Centrality in Convex Amalgamation of Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 6/1 (January 2019), 21-38. https://doi.org/10.13069/jacodesmath.508983.
JAMA Kumar Raghavan Unnithan S, Balakrishnan K. Betweenness centrality in convex amalgamation of graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019;6:21–38.
MLA Kumar Raghavan Unnithan, Sunil and Kannan Balakrishnan. “Betweenness Centrality in Convex Amalgamation of Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 6, no. 1, 2019, pp. 21-38, doi:10.13069/jacodesmath.508983.
Vancouver Kumar Raghavan Unnithan S, Balakrishnan K. Betweenness centrality in convex amalgamation of graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019;6(1):21-38.