Betweenness centrality in Cartesian product of graphs

• Main Authors: Sunil Kumar R., Kannan Balakrishnan
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2020-01-01
• Series: AKCE International Journal of Graphs and Combinatorics
• Subjects: betweenness centrality; pairwise dependency; cartesian product; geodetic graph
• Online Access: http://dx.doi.org/10.1016/j.akcej.2019.03.012

Betweenness centrality is a widely used measure in various graphs and it has a pivotal role in the analysis of complex networks. It measures the potential or power of a node to control the communication over the network. The computation is based on the assumption that information primarily flows over the shortest paths between the nodes of the network. In a graph, the power of a vertex is not an individual attribute, it depends on the influence of other vertices present. Betweenness centrality measures the extent to which a vertex becomes part of the shortest paths between pairs of other vertices in a graph. In this paper, we establish expression for betweenness centrality in Cartesian product of graphs. And investigate the same on certain graphs such as grid, Hamming graphs, hypercubes, Cartesian product of cycles etc.