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Related Experiment Videos

Optimal paths in disordered complex networks.

Lidia A Braunstein1, Sergey V Buldyrev, Reuven Cohen

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review Letters
|November 13, 2003
PubMed
Summary
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We investigated optimal path lengths in networks with random link or node weights. For strong disorder, optimal path length scales with network size N, while weak disorder leads to logarithmic scaling, preserving network properties.

Area of Science:

  • Network science
  • Statistical physics
  • Complex systems

Background:

  • Understanding network properties is crucial for various applications.
  • Disorder in networks, arising from random link or node weights, significantly impacts network behavior.
  • The optimal distance, defined as the path minimizing total weight, is a key metric in disordered networks.

Purpose of the Study:

  • To investigate the optimal distance in networks with varying degrees of disorder.
  • To analyze how network topology (Erdos-Rényi, Watts-Strogatz, scale-free) influences optimal path length under disorder.
  • To determine the scaling behavior of optimal distance with network size (N) under different disorder regimes.

Main Methods:

  • Introduction of disorder by assigning random weights to network links or nodes.

Related Experiment Videos

  • Analysis of optimal distance (l(opt)) in different network models: Erdos-Rényi (ER), Watts-Strogatz (WS), and scale-free (SF).
  • Mathematical derivation and numerical simulations to determine scaling relationships between l(opt) and network size N.

    • Main Results:

    • For strong disorder, l(opt) scales as N(1/3) in ER and WS networks.
    • In SF networks, l(opt) scales as N((lambda-3)/(lambda-1)) for 3=4, disrupting small-world properties.
    • For weak disorder, l(opt) scales as ln(N) across ER, WS, and SF networks, preserving network characteristics.

    Conclusions:

    • The scaling of optimal distance in disordered networks depends on the strength of the disorder and the network's topological properties.
    • Strong disorder can fundamentally alter network behavior, particularly in scale-free networks.
    • Weak disorder maintains the logarithmic scaling of optimal distance, consistent with typical network behavior.