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Block-Preconditioned PageRank for Centrality and Intervention Analysis In Commercial Networks.

Haoran Yin1

  • 1School of Mathematics and Statistics, Jiangsu Normal University; yinhaoran20251@outlook.com.

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|March 30, 2026
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Summary
This summary is machine-generated.

This study introduces a new method to analyze commercial networks, improving how we understand node importance beyond simple financial metrics. The approach enhances network analysis and intervention strategy testing for better business insights.

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Area of Science:

  • Network Science
  • Data Analysis
  • Computational Economics

Background:

  • Commercial networks possess complex structures influenced by diverse factors like geography and business categories.
  • Traditional financial indicators may not fully represent a node's structural significance within these networks.

Purpose of the Study:

  • To develop a robust protocol for constructing and analyzing multi-source commercial networks.
  • To enable reliable computation of PageRank centrality and evaluation of network intervention policies.

Main Methods:

  • Principal component analysis (PCA) for feature extraction and dimensionality reduction.
  • Construction of weighted directed graphs integrating spatial, category, and performance data.
  • Application of a block-preconditioned generalized minimal residual method for PageRank computation.

Main Results:

  • A small number of principal components effectively captured feature variance in retail data.
  • The protocol demonstrated stable directional weighting and reliable PageRank centrality computation.
  • Network intervention simulations showed the impact of reallocating edge weights.

Conclusions:

  • The protocol provides a framework for building interpretable commercial networks from multi-source data.
  • It enables numerically verified centrality measures and reproducible intervention analysis.
  • This method offers valuable tools for understanding and strategizing within complex commercial systems.