Cycle Statistics in Complex Networks and Ihara’s Zeta Function

Clara Grácio; Anthonius Clara Caspar Coolen; Alessia Annibale

doi:10.1007/978-1-4614-9161-3_9

Cycle Statistics in Complex Networks and Ihara’s Zeta Function

Clara Grácio, Anthonius Clara Caspar Coolen, Alessia Annibale

Universidade de Évora

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

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.

Original language	English
Title of host publication	Noninear Maps and their Applications
Subtitle of host publication	Selected Contributions from the NOMA 2011 International Workshop
Editors	Clara Grácio, Daniele Fournier-Prunaret, Tetsushi Ueta, Yoshifumi Nishio
Publisher	Springer New York LLC
Pages	81-94
Volume	57
ISBN (Electronic)	978-1-4614-9161-3
ISBN (Print)	978-1-4614-9160-6
DOIs	https://doi.org/10.1007/978-1-4614-9161-3_9
Publication status	Published - 2014

Publication series

Name	Springer Proceedings in Mathematics and Statistics

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10.1007/978-1-4614-9161-3_9

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Grácio, C., Coolen, A. C. C., & Annibale, A. (2014). Cycle Statistics in Complex Networks and Ihara’s Zeta Function. In C. Grácio, D. Fournier-Prunaret, T. Ueta, & Y. Nishio (Eds.), Noninear Maps and their Applications: Selected Contributions from the NOMA 2011 International Workshop (Vol. 57, pp. 81-94). (Springer Proceedings in Mathematics and Statistics). Springer New York LLC. https://doi.org/10.1007/978-1-4614-9161-3_9

Grácio, Clara ; Coolen, Anthonius Clara Caspar ; Annibale, Alessia. / Cycle Statistics in Complex Networks and Ihara’s Zeta Function. Noninear Maps and their Applications: Selected Contributions from the NOMA 2011 International Workshop. editor / Clara Grácio ; Daniele Fournier-Prunaret ; Tetsushi Ueta ; Yoshifumi Nishio. Vol. 57 Springer New York LLC, 2014. pp. 81-94 (Springer Proceedings in Mathematics and Statistics).

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title = "Cycle Statistics in Complex Networks and Ihara{\textquoteright}s Zeta Function",

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{\textquoteright}s zeta function for counting cycles in networks.",

author = "Clara Gr{\'a}cio and Coolen, {Anthonius Clara Caspar} and Alessia Annibale",

year = "2014",

doi = "10.1007/978-1-4614-9161-3_9",

language = "English",

isbn = "978-1-4614-9160-6",

volume = "57",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "81--94",

editor = "Clara Gr{\'a}cio and Daniele Fournier-Prunaret and Tetsushi Ueta and Yoshifumi Nishio",

booktitle = "Noninear Maps and their Applications",

}

Grácio, C, Coolen, ACC & Annibale, A 2014, Cycle Statistics in Complex Networks and Ihara’s Zeta Function. in C Grácio, D Fournier-Prunaret, T Ueta & Y Nishio (eds), Noninear Maps and their Applications: Selected Contributions from the NOMA 2011 International Workshop. vol. 57, Springer Proceedings in Mathematics and Statistics, Springer New York LLC, pp. 81-94. https://doi.org/10.1007/978-1-4614-9161-3_9

Cycle Statistics in Complex Networks and Ihara’s Zeta Function. / Grácio, Clara; Coolen, Anthonius Clara Caspar ; Annibale, Alessia.
Noninear Maps and their Applications: Selected Contributions from the NOMA 2011 International Workshop. ed. / Clara Grácio; Daniele Fournier-Prunaret; Tetsushi Ueta; Yoshifumi Nishio. Vol. 57 Springer New York LLC, 2014. p. 81-94 (Springer Proceedings in Mathematics and Statistics).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

TY - CHAP

T1 - Cycle Statistics in Complex Networks and Ihara’s Zeta Function

AU - Grácio, Clara

AU - Coolen, Anthonius Clara Caspar

AU - Annibale, Alessia

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1007/978-1-4614-9161-3_9

DO - 10.1007/978-1-4614-9161-3_9

M3 - Conference paper

SN - 978-1-4614-9160-6

VL - 57

T3 - Springer Proceedings in Mathematics and Statistics

SP - 81

EP - 94

BT - Noninear Maps and their Applications

A2 - Grácio, Clara

A2 - Fournier-Prunaret, Daniele

A2 - Ueta, Tetsushi

A2 - Nishio, Yoshifumi

PB - Springer New York LLC

ER -

Grácio C, Coolen ACC , Annibale A. Cycle Statistics in Complex Networks and Ihara’s Zeta Function. In Grácio C, Fournier-Prunaret D, Ueta T, Nishio Y, editors, Noninear Maps and their Applications: Selected Contributions from the NOMA 2011 International Workshop. Vol. 57. Springer New York LLC. 2014. p. 81-94. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-1-4614-9161-3_9

Cycle Statistics in Complex Networks and Ihara’s Zeta Function

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