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Related Concept Videos

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Theories of Dissolution: Diffusion Layer Model

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Related Experiment Video

Updated: May 26, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Percolation transitions are not always sharpened by making networks interdependent.

Seung-Woo Son1, Peter Grassberger, Maya Paczuski

  • 1Complexity Science Group, University of Calgary, Calgary T2N 1N4, Canada.

Physical Review Letters
|December 21, 2011
PubMed
Summary

This study investigates coupled network models. While some networks show abrupt transitions, others, like diluted lattices, exhibit continuous transitions, differing from isolated network behavior.

Related Experiment Videos

Last Updated: May 26, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Coupled network models require nodes to connect via two link types for viability.
  • Previous research suggested coupled networks exhibit more abrupt percolation transitions than uncoupled networks, often found to be discontinuous.
  • The nature of percolation transitions in coupled networks requires further investigation across different network structures.

Purpose of the Study:

  • To analyze the percolation transition in coupled network models.
  • To verify and extend findings on the abruptness of transitions in coupled Erdös-Rényi networks.
  • To investigate the transition behavior in fully interdependent diluted lattices.

Main Methods:

  • Utilized an efficient new algorithm for analyzing network percolation.
  • Simulated node removal in coupled Erdös-Rényi networks and diluted lattices.
  • Calculated the order parameter exponent (β) in 2 and 3 dimensions.

Main Results:

  • Confirmed discontinuous percolation transitions for coupled Erdös-Rényi networks.
  • Discovered continuous percolation transitions for fully interdependent diluted lattices.
  • Observed a larger order parameter exponent (β) in 2D and 3D diluted lattices compared to ordinary percolation, indicating less sharp transitions.

Conclusions:

  • The abruptness of percolation transitions in coupled networks is dependent on the network's specific structure.
  • Fully interdependent diluted lattices exhibit continuous transitions, contrasting with previous claims for coupled systems.
  • Findings suggest that spatially embedded networks may display transition behaviors further from discontinuity than isolated networks.