Abstract Graphs (networks) are an important tool to model data in different domains, including social networks, bioinformatics and the world wide web. Most of the networks formed in these domains are directed graphs, where all the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network G and a vertex r ∈ V (G), we propose a new exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set RV(r), which is used to prune a huge amount of computations that do not contribute in the betweenness score of r. Time complexity of our exact algorithm depends on |RV(r)| and it is respectively for unweighted graphs and weighted graphs with positive weights. |RV(r)| is bounded from above by |V (G)| − 1 and in most cases, it is a small constant. Then, for the cases where RV(r) is large, we present a simple randomized algorithm that samples from RV(r) and performs computations for only the sampled elements. We show that this algorithm provides an (ǫ, δ)-approximation of the betweenness score of r. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that in most cases, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also show that our pro- posed algorithm computes betweenness scores of all vertices in the sets of sizes 5, 10 and 15, much faster and more accurate than the most efficient existing algorithms.
Finally, in REF the authors presented exact and approximate algorithms for computing betweenness centrality of one vertex or a small set of vertices in directed graphs.
Efficient Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs
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