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Cycle Statistics in Complex Networks and Ihara’s Zeta Function

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Nonlinear Maps and their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 57))

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Abstract

Network representations are popular tools for characterizing and visualizing patterns of interaction between the microconstituents of large, complex synthetic, social, or biological systems. They reduce the full complexity of such systems to topological properties of their associated graphs, which are more amenable to analysis. In particular, the cyclic structure of complex networks is receiving increasing attention, since the presence of cycles affects strongly the behavior of processes supported by these networks. In this paper, we survey the analysis of cyclic properties of networks, and in particular the use of Ihara’s zeta function for counting cycles in networks.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Evora, Evora, Portugal

    Clara Grácio

  2. CIMA-UE, Evora, Portugal

    Clara Grácio

  3. Kings College London, London, UK

    Anthony C. C. Coolen & Alessia Annibale

Authors
  1. Clara Grácio
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  2. Anthony C. C. Coolen
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  3. Alessia Annibale
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Corresponding author

Correspondence to Clara Grácio .

Editor information

Editors and Affiliations

  1. Colégio Luís António Verney, University of Évora CIMA-UE, Évora, Portugal

    Clara Grácio

  2. LAAS-INSA, Toulouse, France

    Daniele Fournier-Prunaret

  3. Tokushima University, Tokushima, Japan

    Tetsushi Ueta

  4. E. E. Eng., Tokushima University, Tokushima, Japan

    Yoshifumi Nishio

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Grácio, C., Coolen, A.C.C., Annibale, A. (2014). Cycle Statistics in Complex Networks and Ihara’s Zeta Function. In: Grácio, C., Fournier-Prunaret, D., Ueta, T., Nishio, Y. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9161-3_9

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