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Weighted Distances in Scale-Free Configuration Models.

Erwin Adriaans1, Júlia Komjáthy1

  • 1Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.

Journal of Statistical Physics
|April 2, 2019
PubMed
Summary
This summary is machine-generated.

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This study analyzes first-passage percolation in random graphs with power-law degree distributions. We determine the typical distances in non-explosive branching process scenarios, providing a key result for network analysis.

Area of Science:

  • Random graph theory
  • Network analysis
  • Probability theory

Background:

  • First-passage percolation is studied in the configuration model.
  • Edge weights are assigned i.i.d. (independent and identically distributed).
  • Typical distances (shortest weighted paths) are investigated.

Purpose of the Study:

  • To determine the order of magnitude of typical distances in non-explosive branching process scenarios.
  • To close a gap in understanding for the case.
  • To extend findings to the erased configuration model.

Main Methods:

  • Analysis of first-passage percolation on configuration model graphs.
  • Investigation of age-dependent branching processes approximating local neighborhoods.
Keywords:
Configuration modelFirst passage percolationPower-law degreesRandom networksScale-freeTypical distances

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  • Study of edge-weight distributions, including arbitrary non-continuous ones.

    • Main Results:

    • The first order of magnitude of typical distances is determined for non-explosive branching processes.
    • Typical distances grow with the number of vertices and can be tuned.
    • Results hold for the erased configuration model.

    Conclusions:

    • The study provides a precise understanding of typical distances in a critical regime of random networks.
    • The findings are applicable to networks with power-law degree distributions and specific branching process behaviors.
    • The work extends previous results and offers a tunable way to characterize network distances.