# Faster Betweenness Centrality Updates in Evolving Networks

## TL;DR

This paper introduces a new dynamic algorithm for efficiently updating betweenness centrality in evolving networks after edge insertions or weight decreases, significantly reducing computational operations compared to existing methods.

## Contribution

It presents a novel combination of faster distance and dependency update algorithms for dynamic betweenness centrality, improving efficiency in network analysis.

## Key findings

- Reduces the number of operations in dynamic updates
- Combines two independent improvements for faster updates
- Maintains worst-case complexity equal to recomputation

## Abstract

Finding central nodes is a fundamental problem in network analysis. Betweenness centrality is a well-known measure which quantifies the importance of a node based on the fraction of shortest paths going though it. Due to the dynamic nature of many today's networks, algorithms that quickly update centrality scores have become a necessity. For betweenness, several dynamic algorithms have been proposed over the years, targeting different update types (incremental- and decremental-only, fully-dynamic). In this paper we introduce a new dynamic algorithm for updating betweenness centrality after an edge insertion or an edge weight decrease. Our method is a combination of two independent contributions: a faster algorithm for updating pairwise distances as well as number of shortest paths, and a faster algorithm for updating dependencies. Whereas the worst-case running time of our algorithm is the same as recomputation, our techniques considerably reduce the number of operations performed by existing dynamic betweenness algorithms.