Approximating Betweenness Centrality in Large Evolving Networks

TL;DR

This paper introduces incremental approximation algorithms for betweenness centrality in large, evolving networks, enabling faster computation with guaranteed accuracy and practical in-memory performance for million-edge networks.

Contribution

It presents the first dynamic approximation algorithms with provable error bounds for betweenness centrality in evolving networks.

Findings

Achieves up to 10,000x speedup over static recomputation.

Enables in-memory computation for million-edge networks.

Maintains high accuracy and rank preservation in dynamic settings.

Abstract

Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on randomly sampled paths has been shown to be significantly faster in practice. However, for dynamic networks, no approximation algorithm for betweenness centrality is known that improves on static recomputation. We address this deficit by proposing two incremental approximation algorithms (for weighted and unweighted connected graphs) which provide a provable guarantee on the absolute approximation error. Processing batches of edge insertions, our algorithms yield significant speedups up to a factor of $10^4$ compared to restarting the approximation. This is enabled by investing memory to store and efficiently update shortest paths. As a building block, we also propose an asymptotically faster algorithm for updating the SSSP problem in unweighted graphs. Our experimental study shows that our algorithms are the first to make in-memory computation of a betweenness ranking practical for million-edge semi-dynamic networks. Moreover, our results show that the accuracy is even better than the theoretical guarantees in terms of absolutes errors and the rank of nodes is well preserved, in particular for those with high betweenness.