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Maximizing Closeness in Bipartite Networks: A Graph-Theoretic Analysis

Author

Listed:
  • Fazal Hayat

    (School of Mathematics and Statistics, Gansu Center for Applied Mathematics, Lanzhou University, Lanzhou 730000, China)

  • Daniele Ettore Otera

    (Institute of Data Science and Digital Technologies, Vilnius University, 08412 Vilnius, Lithuania)

Abstract

A fundamental aspect of network analysis involves pinpointing nodes that hold significant positions within the network. Graph theory has emerged as a powerful mathematical tool for this purpose, and there exist numerous graph-theoretic parameters for analyzing the stability of the system. Within this framework, various graph-theoretic parameters contribute to network analysis. One such parameter used in network analysis is the so-called closeness, which serves as a structural measure to assess the efficiency of a node’s ability to interact with other nodes in the network. Mathematically, it measures the reciprocal of the sum of the shortest distances from a node to all other nodes in the network. A bipartite network is a particular type of network in which the nodes can be divided into two disjoint sets such that no two nodes within the same set are adjacent. This paper mainly studies the problem of determining the network that maximize the closeness within bipartite networks. To be more specific, we identify those networks that maximize the closeness over bipartite networks with a fixed number of nodes and one of the fixed parameters: connectivity, dissociation number, cut edges, and diameter.

Suggested Citation

  • Fazal Hayat & Daniele Ettore Otera, 2024. "Maximizing Closeness in Bipartite Networks: A Graph-Theoretic Analysis," Mathematics, MDPI, vol. 12(13), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2039-:d:1426110
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    References listed on IDEAS

    as
    1. Chengli Li & Leyou Xu & Bo Zhou, 2023. "On the residual closeness of graphs with cut vertices," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-24, July.
    2. Dangalchev, Chavdar, 2006. "Residual closeness in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 556-564.
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