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Potential-driven random walks on interconnected systems.

Barbara Benigni1, Riccardo Gallotti2, Manlio De Domenico2

  • 1Department of Information Engineering and Computer Science, University of Trento, Via Sommarive, 9, 38123 Povo, Trento, Italy and CoMuNe Lab, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo, Trento, Italy.

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This study introduces potential-driven random walks to model information routing in complex systems. This new approach bridges the gap between broadcasting and shortest-path routing, offering insights into network navigation and agent movement patterns.

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Area of Science:

  • Complex Systems Science
  • Network Theory
  • Statistical Physics

Background:

  • Interconnected systems rely on information routing, from neural communication to internet protocols.
  • Existing models like random walks and geodesic routing fail to capture complex information flow patterns.
  • A need exists for intermediate routing models that balance broadcasting and shortest-path approaches.

Purpose of the Study:

  • To propose a novel class of stochastic processes for information routing.
  • To develop a framework that interpolates between random walk and geodesic routing.
  • To analyze the impact of network topology on navigation efficiency.

Main Methods:

  • Development of potential-driven random walks based on biased movement.
  • Utilizing a generalized Coulomb potential dependent on distance to destinations.
  • Mathematical modeling and analysis of network heterogeneity and modularity effects.

Main Results:

  • Demonstrated a method to interpolate between random walk and geodesic routing.
  • Showed that network heterogeneity and modularity significantly affect navigation.
  • Illustrated the framework's applicability to animal and human movement patterns.

Conclusions:

  • Potential-driven random walks offer a flexible and effective approach to modeling information routing.
  • No single routing strategy is universally optimal; context-dependent solutions are necessary.
  • This framework provides new analytical tools for network science and agent-based modeling.