Betweenness centrality in convex amalgamation of graphs

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

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