Journal of Statistical Physics

, Volume 118, Issue 3–4, pp 721–734 | Cite as

Continuum Percolation with Unreliable and Spread-Out Connections

  • Massimo Franceschetti
  • Lorna Booth
  • Matthew Cook
  • Ronald Meester
  • Jehoshua Bruck


We derive percolation results in the continuum plane that lead to what appears to be a general tendency of many stochastic network models. Namely, when the selection mechanism according to which nodes are connected to each other, is sufficiently spread out, then a lower density of nodes, or on average fewer connections per node, are sufficient to obtain an unbounded connected component. We look at two different transformations that spread-out connections and decrease the critical percolation density while preserving the average node degree. Our results indicate that real networks can exploit the presence of spread-out and unreliable connections to achieve connectivity more easily, provided they can maintain the average number of functioningconnections per node.


Continuum percolation random connection model Poisson processes stochastic networks unreliable connections 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Massimo Franceschetti
    • 1
    • 4
  • Lorna Booth
    • 2
  • Matthew Cook
    • 2
  • Ronald Meester
    • 3
  • Jehoshua Bruck
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of CaliforniaSan Diego, La JollaUSA
  2. 2.Department of Computation and Neural SystemsCaltechPasadenaUSA
  3. 3.Division of MathematicsVrije Universiteit AmsterdamAmsterdamThe Netherlands
  4. 4.Department of EECSUCBerkeley

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