# KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation

arXiv: https://arxiv.org/abs/1604.08553 · HTML: https://mlsanity.com/paper/1604.08553/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2016.

## Built on by (most cited first, 7 of 7)

- [Parallel and Distributed Graph Neural Networks: An In-Depth Concurrency Analysis](https://mlsanity.com/paper/2205.09702/) (2022)
- [Humans decompose tasks by trading off utility and computational cost](https://mlsanity.com/paper/2211.03890/) (2022)
- [Centrality-Based Node Feature Augmentation for Robust Network Alignment](https://mlsanity.com/paper/2304.12751/) (2023)
- [Edge Ranking of Graphs in Transportation Networks using a Graph Neural Network (GNN)](https://mlsanity.com/paper/2303.17485/) (2023)
- [CLGNN: A Contrastive Learning-based GNN Model for Betweenness Centrality Prediction on Temporal Graphs](https://mlsanity.com/paper/2506.14122/) (2025)
- [Evaluating LLMs on Large-Scale Graph Property Estimation via Random Walks](https://mlsanity.com/paper/2605.01484/) (2026)
- [Graph Neural Networks for Scalable and Transferable Node Centrality Approximation](https://mlsanity.com/paper/2607.09372/) (2026)

## Abstract (arXiv)

We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies on two new theoretical contributions, of independent interest. The first contribution focuses on sampling shortest paths, a subroutine used by most algorithms that approximate betweenness centrality. We show that, on realistic random graph models, we can perform this task in time |E|^frac12+o(1) with high probability, obtaining a significant speedup with respect to the Theta(|E|) worst-case performance. We experimentally show that this new technique achieves similar speedups on real-world complex networks, as well. The second contribution is a new rigorous application of the adaptive sampling technique. This approach decreases the total number of shortest paths that need to be sampled to compute all betweenness centralities with a given absolute error, and it also handles more general problems, such as computing the k most central nodes. Furthermore, our analysis is general, and it might be extended to other settings.