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∣21+o(1)
with high probability, obtaining a significant speedup with respect to the
Θ(∣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.Comment: Some typos correcte