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Shortest paths on systems with power-law distributed long-range connections.
C F Moukarzel1, M Argollo de Menezes
1Departamento de Física Aplicada, CINVESTAV del IPN, Avenue Tecnológico Km. 6, 97310 Mérida, Yucatán, Mexico. cristian@mda.cinvestav.mx
Summary
Shortest-path lengths in complex networks with random long-range links exhibit a characteristic length. Beyond this, path lengths scale differently based on link distribution, revealing distinct network behaviors.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Understanding shortest-path lengths is crucial in analyzing network topology and function.
- Periodic rings with random long-range links present a complex system for path length analysis.
Purpose of the Study:
- To investigate how shortest-path lengths behave in networks with random long-range links.
- To identify characteristic lengths and scaling behaviors in such networks.
- To analyze the impact of link distribution exponent (mu) and density (p) on path lengths.
Main Methods:
- Rescaling arguments applied to network models.
- Numerical simulations on large systems (up to 10^7 sites).
- Analysis of a directed model for comparison.
Main Results:
- A characteristic length (xi) was identified, separating short-range and long-range path behaviors.
- Three distinct scaling regimes (theta(s)=1, 0
- The characteristic length scales with link density (p) as xi ~ p^(-nu), with nu dependent on mu.
Conclusions:
- The shortest-path length in these networks exhibits complex scaling behavior dependent on network parameters.
- The findings provide insights into the structure and navigability of complex networks with long-range connections.
- The study offers a framework for understanding emergent properties in systems with heterogeneous link distributions.