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Updated: May 27, 2026

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

Percolation on correlated random networks.

E Agliari1, C Cioli, E Guadagnini

  • 1Dipartimento di Fisica, Università degli Studi di Parma, Parma, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 9, 2011
PubMed
Summary
This summary is machine-generated.

This study on random, weighted networks reveals that weak ties are crucial for maintaining graph connectivity. Removing these weak links causes gradual network shrinkage rather than abrupt collapse, a finding relevant to social networks.

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Last Updated: May 27, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

  • Network science
  • Statistical physics
  • Complex systems

Background:

  • Hopfield-like models are used to generate random, weighted networks.
  • Percolation theory is a key tool for analyzing network topology and resilience.

Purpose of the Study:

  • To investigate the topological and resilience properties of random, weighted networks.
  • To compare stochastic and deterministic bond percolation in these networks.

Main Methods:

  • Redefinition of patterns in a Hopfield-like model to create weighted networks.
  • Application of stochastic (random) and deterministic (rank-based) bond percolation processes.
  • Analysis of the largest component size and cluster size distribution.

Main Results:

  • Weak ties are essential for maintaining overall graph connectivity.
  • Network collapse is gradual when weak ties are removed, not abrupt.
  • Stochastic and deterministic percolation exhibit different network evolution patterns.

Conclusions:

  • The resilience of weighted networks is highly dependent on the integrity of weak ties.
  • Findings provide insights into the structural behavior of real-world social networks.
  • Understanding percolation dynamics is key to predicting network stability.