[Paper Review] A Faster Algorithm for Betweenness Centrality Based on Adjacency Matrices

Yelai Feng, Huaixi Wang|arXiv (Cornell University)|Apr 30, 2022

Complex Network Analysis Techniques4 citations

TL;DR

This paper proposes a novel betweenness centrality algorithm that leverages parallel computation on adjacency matrices, achieving a time complexity dependent only on the number of nodes rather than edges. It outperforms Brandes' algorithm on small and dense networks and provides a highly efficient solution for large-scale complex networks.

ABSTRACT

Betweenness centrality is essential in complex network analysis; it characterizes the importance of nodes and edges in networks. It is a crucial problem that exactly computes the betweenness centrality in large networks faster, which urgently needs to be solved. We propose a novel algorithm for betweenness centrality based on the parallel computing of adjacency matrices, which is faster than the existing algorithms for large networks. The time complexity of the algorithm is only related to the number of nodes in the network, not the number of edges. Experimental evidence shows that the algorithm is effective and efficient. This novel algorithm is faster than Brandes' algorithm on small and dense networks and offers excellent solutions for betweenness centrality index computing on large-scale complex networks.

Motivation & Objective

• Address the urgent need for faster exact computation of betweenness centrality in large and complex networks.
• Overcome the limitations of existing algorithms, such as Brandes' algorithm, which scale poorly with edge count in dense networks.
• Develop a method that achieves high performance by decoupling time complexity from the number of edges.
• Enable efficient betweenness centrality computation on large-scale, dense, and complex networks through matrix-based parallelism.

Proposed method

• Utilize adjacency matrices as the primary data structure to represent network topology.
• Apply parallel computing techniques to accelerate matrix operations during betweenness centrality computation.
• Design the algorithm so that time complexity scales only with the number of nodes, not the number of edges.
• Leverage the mathematical properties of adjacency matrices to optimize shortest path enumeration and betweenness score aggregation.
• Structure the computation to minimize redundant operations by exploiting matrix symmetry and sparsity patterns.
• Implement the algorithm with a focus on memory access patterns and parallelization efficiency to maximize performance on modern hardware.

Experimental results

Research questions

• RQ1 Can betweenness centrality be computed more efficiently by decoupling time complexity from the number of edges?
• RQ2 How does the performance of the proposed matrix-based algorithm compare to Brandes' algorithm on small and dense networks?
• RQ3 To what extent can parallelization of adjacency matrix operations improve scalability in large-scale complex networks?
• RQ4 Does the proposed method maintain accuracy while significantly reducing computation time compared to existing approaches?

Key findings

• The proposed algorithm achieves a time complexity that depends solely on the number of nodes, not the number of edges, enabling superior scalability.
• Experimental results confirm the algorithm outperforms Brandes' algorithm on small and dense networks due to reduced edge-dependent overhead.
• The method provides an excellent solution for computing betweenness centrality in large-scale complex networks, especially where edge counts are high.
• The use of adjacency matrix parallelism enables significant speedups, particularly in dense network topologies.
• The algorithm maintains exact computation of betweenness centrality without approximation, ensuring accuracy.
• The approach demonstrates strong potential for deployment in real-world network analysis applications requiring high-performance centrality computation.