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Real-world networks show surprisingly stretched paths, not the shortest ones. This finding, confirmed across diverse networks, reveals nature's path selection rules.

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Area of Science:

  • Network Science
  • Complex Systems
  • Data Analysis

Background:

  • Network science has identified universal topological similarities in real-world networks (biological, social, transportation, organizational).
  • Understanding operational paths within these networks is crucial for comprehending their functioning.
  • The 'shortest path assumption' is the prevailing hypothesis for network path structure.

Purpose of the Study:

  • To investigate the actual paths used in real-world networks.
  • To challenge the prevalent shortest path assumption.
  • To identify underlying principles of path selection in complex systems.

Main Methods:

  • Empirical analysis of path structures in four diverse real-world networks.
  • Comparison of actual path lengths against shortest path lengths.
  • Statistical analysis of path stretch distributions.

Main Results:

  • Paths in diverse real-world networks are significantly longer ('stretched') than their shortest counterparts.
  • The distribution of path stretch is remarkably consistent across different network types.
  • Empirical evidence contradicts the universal applicability of the shortest path assumption.

Conclusions:

  • Network path structures deviate substantially from the shortest path hypothesis.
  • A consistent pattern of path stretching exists across various complex systems.
  • Nature employs specific, high-level rules for path selection in networks.