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Correlations between communicability sequence entropy and transport performance in spatially embedded networks.

Dan Chen1, Rui-Wu Niu1, Gui-Jun Pan1

  • 1Faculty of Physics and Electronic Science, Hubei University, Wuhan 430062, China.

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Summary

We found optimal electric current transport in networks when the exponent alpha equals d+1. This condition maximizes network communicability sequence entropy, enhancing transmission efficiency.

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Area of Science:

  • Complex Networks
  • Statistical Physics
  • Network Science

Background:

  • Investigating electric current transport in spatially embedded networks with cost constraints is crucial for understanding network efficiency.
  • Previous work by Li et al. introduced total cost restrictions in such networks.

Purpose of the Study:

  • To determine the optimal conditions for electric current transport in spatially embedded networks with restricted long-range connections.
  • To explore the relationship between network transport performance and communicability sequence entropy.

Main Methods:

  • Constructing d-dimensional regular lattices with added long-range connections.
  • Introducing a probability distribution for long-range connections (P_{ij}∼r_{ij}^{-α}) and restricting total length.
  • Assigning local conductance (g_{ij}∼r_{ij}^{-C}) to network links.
  • Calculating mean effective conductance and communicability sequence entropy for varying exponent α.

Main Results:

  • Optimal electric current transport occurs at α_opt = d+1, irrespective of the conductance exponent C.
  • This optimal condition matches that for best navigation in similar constrained networks.
  • Maximum communicability sequence entropy is achieved when α = d+1.

Conclusions:

  • Network transport performance is strongly correlated with communicability sequence entropy.
  • Maximizing communicability sequence entropy offers an effective strategy for designing high-efficiency power networks.