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A Unified Approach to Percolation Processes on Multiplex Networks

  • Gareth J. BaxterEmail author
  • Davide Cellai
  • Sergey N. Dorogovtsev
  • Alexander V. Goltsev
  • José F. F. Mendes
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each layer having its own kind of edges, represented by different colors. An important fundamental structural feature of networks is their resilience to damage, the percolation transition. Generalization of these concepts to multiplex networks requires careful definition of what we mean by connected clusters. We consider two different definitions. One, a rigorous generalization of the single-layer definition leads to a strong non-local rule, and results in a dramatic change in the response of the system to damage. The giant component collapses discontinuously in a hybrid transition characterized by avalanches of diverging mean size. We also consider another definition, which imposes weaker conditions on percolation and allows local calculation, and also leads to different sized giant components depending on whether we consider an activation or pruning process. This ‘weak’ process exhibits both continuous and discontinuous transitions.

Keywords

Giant Component Hybrid Transition Percolation Transition Pruning Process Multiplex Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partially supported by the FET IP Project MULTIPLEX 317532 and by the FCT projects EXPL/FIS-NAN/1275/2013 and PEst-C/CTM/LA0025/2011, and post-doctoral fellowship SFRH/BPD/74040/2010, Science Foundation Ireland, Grant No. 11/PI/1026 and the FET-Proactive project PLEXMATH (FP7-ICT-2011-8; Grant No. 317614).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gareth J. Baxter
    • 1
    Email author
  • Davide Cellai
    • 2
  • Sergey N. Dorogovtsev
    • 1
    • 3
  • Alexander V. Goltsev
    • 1
    • 3
  • José F. F. Mendes
    • 1
  1. 1.Department of Physics & I3NUniversity of AveiroAveiroPortugal
  2. 2.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland
  3. 3.A. F. Ioffe Physico-Technical InstituteSt. PetersburgRussia

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