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Random walk with memory on complex networks.

Lasko Basnarkov1,2, Miroslav Mirchev1, Ljupco Kocarev1,2

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Summary
This summary is machine-generated.

This study introduces a one-step memory random walk on complex networks. The research provides an exact formula for mean first passage time, revealing optimal random search strategies.

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Area of Science:

  • Complex network analysis
  • Statistical physics
  • Probability theory

Background:

  • Random walks are fundamental tools for analyzing complex networks.
  • Understanding node accessibility and search efficiency is crucial in network science.

Purpose of the Study:

  • To derive an exact expression for mean first passage time in random walks with memory.
  • To investigate the impact of memory on random walk behavior and search strategies.

Main Methods:

  • Utilizing absorbing Markov chains to model the random walk.
  • Developing theoretical expressions for mean first passage time.
  • Conducting numerical experiments on complex networks.

Main Results:

  • An exact formula for mean first passage time was derived for a one-step memory random walk.
  • Numerical results validated the theoretical findings on various network models.
  • A correlation was observed between stationary occupation probability flattening and efficient random search.

Conclusions:

  • The derived formula accurately predicts random walk behavior on networks with memory.
  • The study highlights the potential for memory-enhanced random walks in optimizing search processes.
  • Flattening of stationary occupation probability is a key indicator of near-optimal search performance.