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Two betweenness centrality measures based on Randomized Shortest Paths.

Ilkka Kivimäki1,2, Bertrand Lebichot1, Jari Saramäki2

  • 1Université catholique de Louvain, ICTEAM/LSM, Place des Doyens 1, 1348 Louvain-la-Neuve, Belgium.

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This study introduces novel Randomized Shortest Paths (RSP) betweenness centrality measures. These network analysis tools effectively identify key nodes by optimally combining shortest and random path information.

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Area of Science:

  • Network Science
  • Computational Social Science
  • Data Analysis

Background:

  • Traditional network centrality measures often rely solely on shortest paths.
  • Existing methods may not fully capture node importance by considering random walks or current flows.
  • Randomized Shortest Paths (RSP) framework offers a novel approach to path analysis in networks.

Purpose of the Study:

  • To introduce two new betweenness centrality measures based on the Randomized Shortest Paths (RSP) framework.
  • To bridge the gap between shortest path-based and random walk/current flow-based centrality measures.
  • To enhance the identification of important nodes in complex networks.

Main Methods:

  • Development of two novel betweenness centrality measures derived from the RSP framework.
  • Utilizing Boltzmann probability distributions over network paths, incorporating shortest and longer paths via an inverse temperature parameter.
  • Derivation of computational methods for efficient calculation of the proposed measures.

Main Results:

  • The proposed RSP betweenness centralities optimally combine shortest and random path concepts.
  • Efficient algorithms for computing these new centrality measures are presented.
  • Demonstrated potential in identifying significant network nodes missed by traditional methods through real-world examples.

Conclusions:

  • RSP betweenness centralities offer a powerful new tool for network analysis.
  • These measures provide a more nuanced understanding of node importance compared to traditional methods.
  • The framework has practical applications in identifying key players in real-world networks.