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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Published on: September 8, 2023

Inducing effect on the percolation transition in complex networks.

Jin-Hua Zhao1, Hai-Jun Zhou, Yang-Yu Liu

  • 1State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong-Guan-Cun East Road 55, Beijing 100190, China.

Nature Communications
|September 10, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces an "inducing effect" where nodes outside a connected cluster can cause internal nodes to exit, leading to discontinuous percolation transitions. This framework accurately predicts percolation thresholds and core sizes in complex networks.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Percolation theory traditionally focuses on cluster formation.
  • The influence of external nodes on internal cluster dynamics has been overlooked.
  • Understanding network breakdown phenomena is crucial for various applications.

Purpose of the Study:

  • To investigate the impact of the "inducing effect" on percolation transitions.
  • To develop a theoretical framework for discontinuous breakdown phenomena.
  • To accurately predict percolation thresholds and core sizes in complex networks.

Main Methods:

  • Analysis of classical site percolation and K-core percolation models.
  • Mathematical prediction of percolation thresholds and core sizes.
  • Application to uncorrelated random networks with arbitrary degree distributions.

Main Results:

  • The inducing effect consistently results in discontinuous percolation transitions.
  • Precise predictions for percolation thresholds and core sizes were achieved for random networks.
  • Percolation thresholds showed fluctuations in low-dimensional lattices, but core sizes remained predictable.

Conclusions:

  • The inducing effect provides a novel explanation for discontinuous network breakdown.
  • The developed theoretical framework accurately predicts core sizes in real-world networks using degree distributions.
  • This research offers a quantitative understanding of emergent phenomena in complex systems.