Random walks and flights over connected graphs and complex networks

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23 Scopus citations


Markov chains provide us with a powerful probabilistic tool that allows to study the structure of connected graphs in details. The statistics of events for Markov chains defined on connected graphs can be effectively studied by the method of generalized inverses which we review. The approach is also applicable for directed graphs and interacting networks which share the set of nodes. We discuss a generalization of Lévy flight random walks for large complex networks and study the interplay between the nonlinearity of diffusion process and the topological structure of the network.

Original languageEnglish
Pages (from-to)21-55
Number of pages35
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number1
StatePublished - Jan 2011


  • Complex networks
  • Electrical networks
  • Graph theory
  • Lévy flights
  • Random walks


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