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Explosive percolation in random networks.

Dimitris Achlioptas1, Raissa M D'Souza, Joel Spencer

  • 1Department of Computer Science, University of California at Santa Cruz, Santa Cruz, CA 95064, USA.

Science (New York, N.Y.)
|March 17, 2009
PubMed
Summary
This summary is machine-generated.

Introducing choice into random network formation can cause a discontinuous percolation transition, a novel finding for network science. This challenges previous assumptions about how networks link together near critical points.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Random network formation models, like the Erdös-Rényi model, typically exhibit continuous percolation transitions.
  • Percolation transitions involve a sudden increase in network connectivity around a critical point.
  • The possibility of discontinuous percolation transitions in random networks remained an open theoretical question.

Purpose of the Study:

  • To investigate whether percolation transitions in random networks can be discontinuous.
  • To explore the impact of introducing limited choice into network formation models.
  • To challenge the established understanding of percolation phenomena in random graphs.

Main Methods:

  • Modification of the classic Erdös-Rényi network formation model.
  • Incorporation of a limited choice mechanism into the connection-forming process.
  • Analysis of the resulting network structure and percolation behavior.

Main Results:

  • Demonstration that introducing limited choice leads to a discontinuous percolation transition.
  • Observation of a sudden, large-scale linkage of network components above the transition point.
  • Contrast with the typically continuous transitions observed in purely random models.

Conclusions:

  • Percolation transitions in random networks can be discontinuous under specific conditions.
  • Limited choice in network formation is a key factor driving this discontinuity.
  • Findings offer new insights into the behavior of complex systems and network robustness.