Vertex Betweenness Centrality Of Some Graph Classes With Applications

Abstract

Centrality is an excellent concept for measuring the important or critical vertices in graphs like social networks, biological networks, computer networks etc. Every vertex may be an important vertex from an angle depending on our assumption or how we define the importance. There are different centrality measurements to know the vertex characteristics in a network. Betweenness centrality is a crucial measurement for network analysis based on all shortest paths between each pair of vertices. The betweenness centrality of a node point $v$ is the sum of the ratios between the number of the shortest routes between each pair of other node points that pass through $v$ and the total number of the shortest routes between them. This study describes some new theoretical results related with the measurement of betweenness centrality, relative betweenness centrality and graph betweenness centrality of some special graph classes. In addition, we discuss real-life applications of the results studied in this article.