A New Closeness Centrality Measure based on Minimum Weight Spanning Tree

This paper proposes a simple new measure for closeness centrality for undirected and connected graphs with edge weights. The new closeness centrality measure is based on minimum weight spanning trees and consists of three steps. In the first step, when calculating the absolute closeness centrality, distances from the source vertex to all other vertices are taken as a summation of the edge weights along the shortest path. In the second step, the minimum weight spanning tree is found. In the final step, the normalized closeness measure of a vertex is computed by dividing the total weight of the minimum weight spanning tree by the absolute closeness value (summation of distances of this vertex to other vertices, which is obtained in the first step). This closeness measure is also intrinsically normalized, always giving a value between ‘0’ (lowest closeness value) and ‘1’ (highest closeness value). As this closeness measure is normalized, considers the edge weights, and is based on the minimum weight spanning tree, it is useful for real-world applications.