Graph Entropy from Closed Walk and Cycle Functionals

  • Furqan AzizEmail author
  • Edwin R. Hancock
  • Richard C. Wilson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10029)


This paper presents an informational functional that can be used to characterise the entropy of a graph or network structure, using closed random walks and cycles. The work commences from Dehmer’s information functional, that characterises networks at the vertex level, and extends this to structures which capture the correlation of vertices, using walk and cycle structures. The resulting entropies are applied to synthetic networks and to network time series. Here they prove effective in discriminating between different types of network structure, and detecting changes in the structure of networks with time.


Graph entropy Random walks Ihara coefficients 


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Furqan Aziz
    • 1
    Email author
  • Edwin R. Hancock
    • 2
  • Richard C. Wilson
    • 2
  1. 1.Department of Computer ScienceIM—SciencesPeshawarPakistan
  2. 2.Department of Computer ScienceUniversity of YorkYorkUK

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