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Small-world networks: links with long-tailed distributions

Jespersen1, Blumen

  • 1Institute of Physics and Astronomy, University of Aarhus, DK-8000 Arhus C, Denmark and Theoretische Polymerphysik, Universitat Freiburg, D-79104 Freiburg im Breisgau, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
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Summary

This study introduces a novel small-world network (SWN) model where link probability depends on chemical distance. This research explores random walker behavior and its connection to Levy flights in these complex networks.

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Area of Science:

  • Complex networks
  • Statistical physics
  • Network science

Background:

  • Small-world networks (SWN) are crucial for modeling complex systems.
  • Existing SWN models often use uniform random link additions.
  • Understanding network dynamics requires exploring novel network structures.

Purpose of the Study:

  • To introduce and analyze a new variant of small-world networks.
  • To investigate the impact of chemically dependent link probabilities on network properties.
  • To study the behavior of random walkers on these modified networks.

Main Methods:

  • Development of a physical model for small-world networks with distance-dependent link probability.
  • Assumption of a power-law probability distribution for additional links (AL).
  • Analysis of random walker behavior, specifically the probability of return to the origin.

Main Results:

  • The probability of random walkers returning to the origin is analyzed.
  • A connection is established between the model's outcomes and Levy flights.
  • The study highlights how chemical distance influences network topology and dynamics.

Conclusions:

  • The proposed SWN variant offers a new perspective on network construction.
  • Random walker behavior is significantly affected by chemically dependent link probabilities.
  • The findings provide insights into phenomena related to Levy flights in complex systems.