Vertex Betweenness Centrality of Corona Graphs and Unicyclic Graphs

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 (Pn⊙Pm, Pn⊙Km, Cn⊙Km, Cn⊙Pm, Cn⊙Cm and Cn⊙Kl,m) and unicyclic graphs (A(n, k, l), B(n, k, l), D(n, k, l) and E(n, k, l)).