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Alternative expression of message passing on networks.

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  • 1Data Insights AI, CodeBase Edinburgh, Argyle House, 3 Lady Lawson Street, Edinburgh EH3 9DR, United Kingdom.

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We present a novel message-passing method for network analysis, offering an alternative to standard approaches for calculating the largest connected component in bond percolation. This new technique also provides insights into local network environments and generalizes to various percolation models.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • Message-passing techniques are state-of-the-art for analyzing network properties.
  • These methods are crucial for understanding networked systems across various scientific domains.
  • A key application is determining the largest connected component in bond percolation.

Purpose of the Study:

  • Introduce an alternative message-passing method for network analysis.
  • Develop a new approach to calculate the size of the largest connected component in bond percolation.
  • Explore the method's applicability to generalized percolation models and local network environments.

Main Methods:

  • Developed a novel message-passing algorithm for network property ascertainment.
  • The method is exact on tree networks and provides approximations for general graphs.
  • Investigated the method's performance on sequential and nonbinary percolation models.

Main Results:

  • The proposed method accurately determines the largest connected component size on trees.
  • It serves as an approximation for arbitrary graphs, offering an alternative to existing techniques.
  • The method successfully generalizes to various percolation scenarios, including sequential and nonbinary percolation.

Conclusions:

  • The new message-passing approach offers a valuable alternative for network analysis, particularly in bond percolation.
  • It provides richer information about local network structures compared to traditional methods.
  • The method's flexibility extends its utility to a broader range of network percolation problems.