An Efficient Heuristic for Betweenness-Ordering

TL;DR

This paper introduces a fast heuristic algorithm for ordering vertices by betweenness centrality in large networks, avoiding exact calculations and leveraging a non-uniform sampling model based on Erdos-Renyi graph analysis.

Contribution

The paper presents a novel heuristic that efficiently determines betweenness-ordering of a small vertex subset without exact computation, outperforming existing methods in speed and accuracy.

Findings

Efficient betweenness-ordering achieved in linear time relative to edges.

The heuristic outperforms existing techniques in synthetic and real-world networks.

Non-uniform node sampling based on Erdos-Renyi graphs underpins the approach.

Abstract

Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen broad and increasing applications across several disciplines of late. Amongst a plethora of application specific definitions available in the literature to rank the vertices, closeness centrality, betweenness centrality and eigenvector centrality (page-rank) have been the most important and widely applied ones. Networks where information, signal or commodities are flowing on the edges, surrounds us. Betweenness centrality comes as a handy tool to analyze such systems, but betweenness computation is a daunting task in large size networks. In this paper, we propose an efficient heuristic to determine the betweenness-ordering of $k$ vertices (where $k$ is very less than the total number of vertices) without computing their exact betweenness indices. The algorithm is based on a non-uniform node sampling model which is developed based on the analysis of Erdos-Renyi graphs. We apply our approach to find the betweenness-ordering of vertices in several synthetic and real-world graphs. The proposed heuristic results very efficient ordering even when runs for a linear time in the terms of the number of edges. We compare our method with the available techniques in the literature and show that our method produces more efficient ordering than the currently known methods.