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The Degree Distribution of Networks: Statistical Model Selection

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Bacterial Molecular Networks

Part of the book series: Methods in Molecular Biology ((MIMB,volume 804))

Abstract

The degree distribution has been viewed as an important characteristic of network data. Many biological networks have been labelled scale-free as their degree distribution can be approximately described by a power-law probability distribution. This chapter presents a formal statistical model selection procedure that can determine which functional form, from a collection of specified models, best describes the degree distribution of network data. The degree distribution found for empirical data is viewed as belonging to a class of probability models and the model which best describes the data is determined in a maximum likelihood framework. In conclusion, it is important to note that these statistical tests do not confirm the true underlying distribution of the observed data, but instead show which models from a chosen set best describe the data. In reality, these approaches should be viewed as providing evidence for which probability models do not adequately (or optimally) describe the data, and give an indication of the underlying sampling and true interaction properties of the system considered.

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Acknowledgments

This work has been funded by the Wellcome Trust and the BBSRC. MPHS is a Royal Society Wolfson Research Merit Award holder.

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Authors and Affiliations

  1. Theoretical Systems Biology group, Imperial College, London, UK

    William P. Kelly & Michael P. H. Stumpf

  2. Department of Mathematics, Imperial College, South Kensington Campus, London, UK

    Piers J. Ingram

Authors
  1. William P. Kelly
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  2. Piers J. Ingram
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  3. Michael P. H. Stumpf
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Corresponding author

Correspondence to Michael P. H. Stumpf .

Editor information

Editors and Affiliations

  1. Labo. Bioinformatique des, Génomes et des Réseaux (BiGRe), Université Libre de Bruxelles, bd. du Triomphe, Bruxelles, 1050, Belgium

    Jacques van Helden

  2. Labo. Bioinformatique des, Génomes et des Réseaux (BiGRe), Université Libre de Bruxelles, Bvd. du Triomphe, Bruxelles, 1050, Belgium

    Ariane Toussaint

  3. INSERM 1024, Institut de Biologie de l'Ecole Normale, rue d'Ulm 46, Paris, 75230, France

    Denis Thieffry

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Kelly, W.P., Ingram, P.J., Stumpf, M.P.H. (2012). The Degree Distribution of Networks: Statistical Model Selection. In: van Helden, J., Toussaint, A., Thieffry, D. (eds) Bacterial Molecular Networks. Methods in Molecular Biology, vol 804. Springer, New York, NY. https://doi.org/10.1007/978-1-61779-361-5_13

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  • DOI: https://doi.org/10.1007/978-1-61779-361-5_13

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-61779-360-8

  • Online ISBN: 978-1-61779-361-5

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