Betweenness centrality in convex amalgamation of graphs

Year 2019, Volume: 6 Issue: 1, 21 - 38, 19.01.2019

Sunil Kumar Raghavan Unnithan Kannan Balakrishnan

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.

Keywords

Betweenness centrality, Central vertex, Extreme vertex, Convex subgraph, Vertex amalgamation, Edge amalgamation, Path amalgamation, Subgraph amalgamation

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.