Electronic Journal of Statistics

Detecting local network motifs

Etienne Birmelé

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Studying the structure of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are partially built from small functional units called motifs, which can be found by looking for small subgraphs whose numbers of occurrences in the whole network are surprisingly high. In this article, we propose to define motifs through a local over-representation in the network and develop a statistic to detect them without relying on simulations. We then illustrate the performance of our procedure on simulated and real data, recovering already known biologically relevant motifs. Moreover, we explain how our method gives some information about the respective roles of the vertices in a motif.

Article information

Electron. J. Statist. Volume 6 (2012), 908-933.

First available in Project Euclid: 21 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62P10: Applications to biology and medical sciences
Secondary: 05C90: Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]

Network motif Poisson approximation biological network


Birmelé, Etienne. Detecting local network motifs. Electron. J. Statist. 6 (2012), 908--933. doi:10.1214/12-EJS698. https://projecteuclid.org/euclid.ejs/1337604769.

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