Fast Approximated Betweenness Centrality of Directed and Weighted Graphs

  • Angelo FurnoEmail author
  • Nour-Eddin El Faouzi
  • Rajesh Sharma
  • Eugenio Zimeo
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)


Node betweenness centrality is a reference metric to identify the most critical spots of a network. However, its exact computation exhibits already high (time) complexity on unweighted, undirected graphs. In some domains such as transportation, weighted and directed graphs can provide more realistic modeling, but at the cost of an additional computation burden that limits the adoption of betweenness centrality for real-time monitoring of large networks. As largely demonstrated in previous work, approximated approaches represent a viable solution for continuous monitoring of the most critical nodes of large networks, when the knowledge of the exact values is not necessary for all the nodes.

This paper presents a fast algorithm for approximated computation of betweenness centrality for weighted and directed graphs. It is a substantial extension of our previous work which focused only on unweighted and undirected networks. Similarly to that, it is based on the identification of pivot nodes that equally contribute to betweenness centrality values of the other nodes of the network. The pivots are discovered via a cluster-based approach that permits to identify the nodes that have the same properties with reference to clusters’ border nodes. The results prove that our algorithm exhibits significantly lower execution time and a bounded and tolerable approximation with respect to state-of-the-art approaches for exact computation when applied to very large, weighted and directed graphs.


Betweenness centrality Directed weighted graphs Fast computation Large scale networks Real-time monitoring 



This work has been supported by the French research project PROMENADE (grant number ANR-18-CE22-0008), the H2020 framework project SoBigData, grant number 654024, and the GAUSS project (MIUR, PRIN 2015, Contract 2015KWREMX).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Angelo Furno
    • 1
    Email author
  • Nour-Eddin El Faouzi
    • 1
  • Rajesh Sharma
    • 2
  • Eugenio Zimeo
    • 3
  1. 1.University of Lyon, IFSTTAR, ENTPE, LICIT UMR_T9401LyonFrance
  2. 2.University of TartuTartuEstonia
  3. 3.University of SannioBeneventoItaly

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