Directed Network as a Chaotic Dynamical System

  • Syuji Miyazaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4012)


A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius-Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large-deviation properties of local expansion rates (finite-time Lyapunov exponents) related to chaotic dynamics, we can also discuss those properties of network structure.


Lyapunov Exponent Chaotic Dynamic Directed Network Deterministic Chaos Left Eigenvector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Syuji Miyazaki
    • 1
  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan

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