Construction of some betweenness uniform graphs

The betweenness centrality of a graph measures the tendency of a single vertex to be more central than all other vertices in the graph. It is based on differences between the centrality of the most central vertex and that of all others. In many real world situations it has quite a significant role. In this paper, we initiate the study of betweenness uniform centrality of some graphs and investigate how to construct a betweenness uniform graph for a given betweenness centrality.