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

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.