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Time-dependent personalized PageRank for temporal networks: Discrete and continuous scales.

David Aleja1,2,3,4, Julio Flores1, Eva Primo1,2

  • 1Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, 28933 Móstoles (Madrid), Spain.

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This study introduces time-varying PageRank for evolving networks, showing discrete sampling accurately estimates continuous temporal network PageRank. It precisely bounds personalization vector influence on node ranking.

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Area of Science:

  • Network Science
  • Computer Science
  • Data Analysis

Background:

  • Temporal networks, which change over time, present unique challenges for ranking algorithms like PageRank.
  • Existing PageRank methods often assume static network structures, limiting their applicability to dynamic systems.

Purpose of the Study:

  • To introduce and analyze a time-dependent PageRank algorithm for temporal networks.
  • To investigate the impact of time-varying network topology, damping factors, and personalization vectors on node rankings.
  • To provide theoretical bounds on the influence of personalization vectors in temporal networks.

Main Methods:

  • Developed a PageRank formulation for continuous-time temporal networks.
  • Analyzed the relationship between continuous-time and discrete-time temporal network PageRank through sampling.
  • Established theoretical bounds for the influence of time-dependent personalization vectors on node importance.

Main Results:

  • Demonstrated that PageRank of continuous-temporal networks can be accurately estimated using discrete-time samples.
  • Provided precise boundaries for the influence of personalization vectors on individual node rankings.
  • Showcased the independent time-variability of network topology, damping factor, and personalization vectors in PageRank.

Conclusions:

  • The proposed time-dependent PageRank offers a robust method for analyzing dynamic networks.
  • Discrete sampling provides a reliable approximation for continuous temporal network analysis.
  • This work advances the understanding of ranking in evolving network structures.