Abstract
In this paper, first given a directed network G and a vertex \(r \in V(G)\), we propose a new exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set \(\mathcal {RF}(r)\), which is used to prune a huge amount of computations that do not contribute in the betweenness score of r. Then, for the cases where \(\mathcal {RF}(r)\) is large, we present a randomized algorithm that samples from \(\mathcal {RF}(r)\) and performs computations for only the sampled elements. We show that this algorithm provides an \((\epsilon ,\delta )\)-approximation of the betweenness score of r. Finally, we empirically evaluate our algorithms and show that they significantly outperform the most efficient existing algorithms, in terms of both running time and accuracy. Our experiments also show that our proposed algorithms can effectively compute betweenness scores of all vertices in a set of vertices.
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Notes
- 1.
For given values of \(\epsilon \) and \(\delta \), KADABRA computes the normalized betweenness of the vertices of the graph within an error \(\epsilon \) with a probability at least \(1-\delta \). The normalized betweenness of a vertex is its betweenness score divided by \(n\cdot \left( n-1\right) \). Therefore, we multiply the scores computed by KADABRA by \(n\cdot \left( n-1\right) \).
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This work has been supported by the ANR project IDOLE.
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Chehreghani, M.H., Bifet, A., Abdessalem, T. (2018). Efficient Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs. In: Phung, D., Tseng, V., Webb, G., Ho, B., Ganji, M., Rashidi, L. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2018. Lecture Notes in Computer Science(), vol 10939. Springer, Cham. https://doi.org/10.1007/978-3-319-93040-4_59
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