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<p>We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control (through network modifications) and parametric control (through measure parameters) of these centralities. We characterize the conditions for complete control of centrality scores and the weaker notion of ranking control, establishing bounds for the required parameters. Our analysis includes classical PageRank alongside two generalizations: node-dependent dampings and node-dependent personalization vector, with the latter being an idea rarely discussed in the literature. We examine how their underlying random walk structures affect their controllability, providing insights into how parameter variations can influence node importance hierarchies. These results advance our understanding of the interplay between algebraic control and stochastic dynamics in network centrality measures.</p>

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Fully personalized PageRank and algebraic methods to distribute a random walker

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Gonzalo Contreras-Aso,
  • Regino Criado,
  • Miguel Romance

摘要

We present a comprehensive analysis of algebraic methods for controlling the stationary distribution of PageRank-like random walkers. Building upon existing literature, we compile and extend results regarding both structural control (through network modifications) and parametric control (through measure parameters) of these centralities. We characterize the conditions for complete control of centrality scores and the weaker notion of ranking control, establishing bounds for the required parameters. Our analysis includes classical PageRank alongside two generalizations: node-dependent dampings and node-dependent personalization vector, with the latter being an idea rarely discussed in the literature. We examine how their underlying random walk structures affect their controllability, providing insights into how parameter variations can influence node importance hierarchies. These results advance our understanding of the interplay between algebraic control and stochastic dynamics in network centrality measures.