A Divide-and-Conquer Algorithm for Betweenness Centrality

TL;DR

This paper introduces Brandes++, a novel divide-and-conquer algorithm that efficiently computes betweenness centrality by creating a simplified graph sketch called a skeleton, significantly reducing computation time on real-world datasets.

Contribution

We propose Brandes++, an exact algorithm that leverages graph skeletons to improve efficiency over previous methods for betweenness centrality computation.

Findings

Achieves lower running times on various real-world graphs.

Demonstrates effectiveness across different graph structures.

Provides publicly available implementation for research use.

Abstract

The problem of efficiently computing the betweenness centrality of nodes has been researched extensively. To date, the best known exact and centralized algorithm for this task is an algorithm proposed in 2001 by Brandes. The contribution of our paper is Brandes++, an algorithm for exact efficient computation of betweenness centrality. The crux of our algorithm is that we create a sketch of the graph, that we call the skeleton, by replacing subgraphs with simpler graph structures. Depending on the underlying graph structure, using this skeleton and by keeping appropriate summaries Brandes++ we can achieve significantly low running times in our computations. Extensive experimental evaluation on real life datasets demonstrate the efficacy of our algorithm for different types of graphs. We release our code for benefit of the research community.