Betweenness-based Ranking of Edges using the Principal Components of the Complements of Local Clustering Coefficient and Neighborhood Overlap

Edge betweenness centrality (EBWC) is a computationally-heavy metric used to quantify the contribution of edges for communicating on shortest paths between any two vertices in a network. In this paper, we explore the use of metrics such as the local clustering coefficient (LCC) of a node and the neighborhood overlap (NOVER) scores of the edges as the basis to quantify the contribution of edges for communicating on shortest paths. As vertices with lower LCC and edges with lower NOVER are expected to be unused by their neighbors (and hence unused by any other node in the network as well) and vice-versa for communicating on shortest paths, we propose to develop a principal components analysis (PCA)-based composite betweenness scores for the edges (referred to as PCA_EBW) computed on the basis of a dataset that includes the LCC' (1-LCC) values for the end vertices and the NOVER' (1-NOVER) scores for the edges. When applied over a diverse collection of real-world networks, we notice a moderate-strong Spearman's rank-based correlation between the PCA-EBW scores for the edges and their EBWC values.