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## Betweenness centrality in convex amalgamation of graphs

#### Sunil Kumar Raghavan Unnithan [1] , Kannan Balakrishnan [2]

##### 17 58

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.
Betweenness centrality, Central vertex, Extreme vertex, Convex subgraph, Vertex amalgamation, Edge amalgamation, Path amalgamation, Subgraph amalgamation
• [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.
Primary Language en Engineering Articles Orcid: 0000-0002-8254-6511Author: Sunil Kumar Raghavan Unnithan (Primary Author) Author: Kannan Balakrishnan
 Bibtex @research article { jacodesmath508983, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {Yildiz Technical University}, year = {2019}, volume = {6}, pages = {21 - 38}, doi = {10.13069/jacodesmath.508983}, title = {Betweenness centrality in convex amalgamation of graphs}, key = {cite}, author = {Kumar Raghavan Unnithan, Sunil and Balakrishnan, Kannan} } 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. DOI: 10.13069/jacodesmath.508983 MLA Kumar Raghavan Unnithan, S , Balakrishnan, K . "Betweenness centrality in convex amalgamation of graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019): 21-38 Chicago Kumar Raghavan Unnithan, S , Balakrishnan, K . "Betweenness centrality in convex amalgamation of graphs". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019): 21-38 RIS TY - JOUR T1 - Betweenness centrality in convex amalgamation of graphs AU - Sunil Kumar Raghavan Unnithan , Kannan Balakrishnan Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.508983 DO - 10.13069/jacodesmath.508983 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 21 EP - 38 VL - 6 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.508983 UR - https://doi.org/10.13069/jacodesmath.508983 Y2 - 2018 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Betweenness centrality in convex amalgamation of graphs %A Sunil Kumar Raghavan Unnithan , Kannan Balakrishnan %T Betweenness centrality in convex amalgamation of graphs %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 1 %R doi: 10.13069/jacodesmath.508983 %U 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