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Statistical-mechanical iterative algorithms on complex networks.

Jun Ohkubo1, Muneki Yasuda, Kazuyuki Tanaka

  • 1Department of System Information Sciences, Graduate School of Information Sciences, Tohoku University, 6-3-09, Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan. jun@smapip.is.tohoku.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
PubMed
Summary

This study examines a statistical-mechanical iterative algorithm for minimizing Bethe free energy on complex networks. Prioritizing high-degree nodes improves algorithm performance on scale-free networks like Barabási-Albert, but not random networks like Erdös-Rényi.

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Area of Science:

  • Statistical mechanics
  • Network science
  • Information theory

Background:

  • Ising models are used across information and social sciences.
  • Minimizing Bethe free energy is key to solving many Ising model problems.
  • Statistical-mechanical iterative algorithms are commonly employed for this minimization.

Purpose of the Study:

  • To investigate the impact of complex network heterogeneity on a statistical-mechanical iterative algorithm.
  • To develop and test an enhanced iterative algorithm that incorporates network heterogeneity information.

Main Methods:

  • Studied a statistical-mechanical iterative algorithm on complex networks.
  • Introduced a modified algorithm prioritizing updates for higher-degree nodes.
  • Conducted numerical experiments on Barabási-Albert and Erdös-Rényi networks.

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Main Results:

  • The enhanced algorithm's performance was affected by heterogeneity in Barabási-Albert networks.
  • The algorithm's performance was not influenced by heterogeneity in Erdös-Rényi networks.
  • High-degree nodes in scale-free networks facilitate rapid information propagation.

Conclusions:

  • Network heterogeneity significantly impacts the iterative algorithm's efficiency.
  • Prioritizing high-degree nodes is beneficial for scale-free networks but not random networks.
  • The structure of complex networks, particularly scale-free ones, plays a crucial role in information propagation dynamics.