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Characterizing network topology using first-passage analysis.

M S Chaves1, T G Mattos2, A P F Atman3

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This study uses first-passage analysis to explore how network topology impacts navigability. The findings help differentiate network types, including random and scale-free networks, based on walker behavior.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Statistical Physics

Background:

  • Understanding complex network topology is crucial for diverse fields like economics, biology, and sociology.
  • Network navigability, influenced by topological characteristics, is a key area of scientific inquiry.
  • First-passage analysis offers a powerful lens to study random walker behavior in networks.

Purpose of the Study:

  • To investigate network properties and random walker characteristics across varying topologies.
  • To differentiate network types, particularly random versus scale-free networks, based on navigability metrics.
  • To demonstrate the utility of first-passage analysis in characterizing network structures and behaviors.

Main Methods:

  • Employed first-passage analysis tools to study random walkers on networks.
  • Systematically modified a 2D square lattice topology by random link reconnections.
  • Measured first-passage time, first-passage simultaneity, and site occupancy statistics for random walkers.

Main Results:

  • Successfully differentiated network topologies, distinguishing random from scale-free networks via walker dynamics.
  • Demonstrated that first-passage measures effectively characterize network navigability.
  • Showcased the ability of the proposed technique to highlight small-world network features.

Conclusions:

  • First-passage analysis provides a robust method for assessing network navigability and topological features.
  • The study successfully distinguishes between different complex network types based on walker behavior.
  • This approach offers valuable insights into the structure-function relationships in complex systems.