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Distance distribution in configuration-model networks.

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Summary
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We analyzed shortest path lengths in random networks using recursion equations. Our findings align with simulations, revealing key network properties and their relationship to degree distributions.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Graph Theory

Background:

  • Understanding network structure is crucial in various fields.
  • Shortest path lengths are fundamental network metrics.
  • Configuration model networks provide a framework for studying random graph properties.

Purpose of the Study:

  • To derive analytical results for shortest path length distributions in configuration model networks.
  • To investigate the relationship between degree distributions and shortest path lengths.
  • To evaluate central and dispersion measures of shortest path lengths.

Main Methods:

  • Utilized recursion equations to derive analytical expressions.
  • Compared analytical results with numerical simulations.
  • Analyzed networks with degenerate, binomial, and power-law degree distributions.

Main Results:

  • Analytical results for shortest path length distributions show good agreement with numerical simulations.
  • Expressions for the mean, mode, and variance of shortest path lengths were derived.
  • Established clear connections between degree distribution moments and shortest path length measures.

Conclusions:

  • The study provides a robust analytical framework for shortest path lengths in random networks.
  • The findings highlight the impact of degree distributions on network topology.
  • This work offers insights into network characterization and comparison.