Vertex Betweenness Centrality of Corona Graphs and Unicyclic Graphs

Abstract

The idea of centrality measurements is quite appropriate for determining the important vertices or edges in a network. A vertex in a network may be an important vertex depending on its angle of assumption. There are many centrality measurements to find the characteristics of a vertex in a network. Betweenness centrality is an important variant of centrality measurement for analyzing complex networks based on shortest paths. The betweenness centrality of a node point $u$ is the sum of the fraction which has the number of shortest paths between any two node points $v$ and $w$ as denominator and the number of the shortest paths passing through the vertex $u$ between them as numerator. This paper describes some theoretical results relating to the betweenness centrality and relative betweenness centrality of different types of corona graphs ($P_{n}\odot P_{m}$, $P_{n}\odot K_{m}$, $C_{n}\odot K_{m}$, $C_{n}\odot P_{m}$, $C_{n}\odot C_{m}$ and $C_{n}\odot K_{l,m}$) and unicyclic graphs ($A(n, k, l)$, $B(n,k,l)$, $D(n,k,l)$ and $E(n,k,l)$).