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Related Experiment Video

Updated: Feb 28, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Multiple random walks on complex networks: A harmonic law predicts search time.

Tongfeng Weng1, Jie Zhang2, Michael Small3,4

  • 1HKUST-DT System and Media Laboratory, Hong Kong University of Science and Technology, 999077, Hong Kong.

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Multiple random walks on complex networks achieve efficient target search. The study introduces mean first parallel passage time (MFPPT), revealing a universal harmonic law for search efficiency across diverse network structures.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Random walks are fundamental models for exploring networks.
  • Quantifying the efficiency of multiple searchers is crucial in various applications.
  • Existing metrics often focus on single walker efficiency.

Purpose of the Study:

  • To introduce and define the mean first parallel passage time (MFPPT) for multiple random walkers.
  • To develop a general analytical theory for calculating MFPPT on complex networks.
  • To uncover universal principles governing parallel search strategies.

Main Methods:

  • Analytical derivation of MFPPT.
  • Theoretical modeling of random walks on networks.
  • Numerical simulations on synthetic and real-world networks.

Main Results:

  • A general theory for calculating MFPPT is established.
  • Global MFPPT follows a harmonic law with respect to individual walker passage times.
  • Identical walkers exhibit power-law decay of MFPPT with exponent unity, independent of network topology.

Conclusions:

  • The harmonic law provides a universal principle for multiple random walk search efficiency.
  • MFPPT effectively quantifies the collective search performance of multiple walkers.
  • The framework is applicable to a wide range of parallel random search processes.