In this paper, we consider a simple connected graph having no loops and multiple edges. The order and size of are denoted by and respectively in graphs is a wide branch of graph theory having many scientific and real-life applications. There are various types of distances studied in the literature.The distance is the length of the shortest path between the vertices and in [2]. The detour distance is the length of the longest path between the vertices and in [3]. The concept of centrality widely applied in social network analysis. Degree centrality is the simplest centrality measure to compute centre. Betweenness centrality measures used for analyzed cancer network.