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Long-loop feedback vertex set and dismantling on bipartite factor graphs.

Tianyi Li1,2, Pan Zhang1,3,4, Hai-Jun Zhou1,5,6

  • 1CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

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Summary

Network dismantling, crucial for network analysis, is improved by a new framework. This approach distinguishes local clusters from long loops, enhancing algorithm performance for better network breakdown.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • Network dismantling aims to disconnect networks by targeting vertices within loops.
  • Current loop-focused methods struggle with distinguishing local clusters from long-range connections, reducing efficiency.
  • This limitation hinders optimal network dismantling strategies.

Purpose of the Study:

  • To introduce a novel framework for network dismantling that improves upon existing loop-focused strategies.
  • To enhance the performance of network dismantling algorithms by addressing the limitations of current approaches.
  • To develop a more effective method for identifying critical vertices in complex networks.

Main Methods:

  • A two-scale bipartite factor-graph representation is proposed to differentiate local clusters and long loops.
  • Local dense clusters are simplified as individual factor nodes, while long loops are preserved.
  • Mean-field spin-glass theory is applied to solve the long-loop feedback vertex set problem.

Main Results:

  • The proposed framework successfully distinguishes between short, local loops and long, inter-cluster loops.
  • New versions of benchmark algorithms, BPD (using spin-glass theory solvers) and CoreHD, show significant performance improvements.
  • The developed solvers outperform current state-of-the-art algorithms across various network types.

Conclusions:

  • The new two-scale bipartite factor-graph framework offers a superior approach to network dismantling.
  • Distinguishing loop scales is key to enhancing dismantling efficiency and algorithm performance.
  • Flexible selection of local clusters offers further potential for improving dismantling outcomes.