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Influence Maximization Dynamics and Topological Order on Erdös-Rényi Networks

Author

Listed:
  • J. Leonel Rocha

    (CEAUL and Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal)

  • Sónia Carvalho

    (CEAUL and Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal)

  • Beatriz Coimbra

    (CEAUL and Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal)

  • Inês Henriques

    (Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal)

  • Juliana Pereira

    (Department of Mathematics of ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal)

Abstract

This paper concerns the study of the linear threshold model in random networks, specifically in Erdös-Rényi networks. In our approach, we consider an activation threshold defined by the expected value for the node degree and the associated influence activation mapping. According to these assumptions, we present a theoretical procedure for the linear threshold model, under fairly general conditions, regarding the topological structure of the networks and the activation threshold. Aiming at the dynamics of the influence maximization process, we analyze and discuss different choices for the seed set based on several centrality measures along with the state conditions for the procedure to trigger. The topological entropy established for Erdös-Rényi networks defines a topological order for this type of random networks. Sufficient conditions are presented for this topological entropy to be characterized by the spectral radius of the associated adjacency matrices. Consequently, a number of properties are proved. The threshold dynamics are analyzed through the relationship between the activation threshold and the topological entropy. Numerical studies are included to illustrate the theoretical results.

Suggested Citation

  • J. Leonel Rocha & Sónia Carvalho & Beatriz Coimbra & Inês Henriques & Juliana Pereira, 2023. "Influence Maximization Dynamics and Topological Order on Erdös-Rényi Networks," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3299-:d:1203485
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    References listed on IDEAS

    as
    1. J. Leonel Rocha & J. Sousa Ramos, 2004. "Weighted kneading theory of one-dimensional maps with a hole," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-20, January.
    2. Lin Zhang & Kan Li, 2022. "Influence Maximization Based on Snapshot Prediction in Dynamic Online Social Networks," Mathematics, MDPI, vol. 10(8), pages 1-20, April.
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