Determination of Z-score and P-value for network motifs

Z-score and P-value of a motif are measures of its statistical significance for a particular network. The Z-score is defined as the difference of the frequency of this motif (concept F1) in the target network and its mean frequency in a sufficiently large set of randomised networks, divided by the standard deviation of the frequency values for the randomised networks [2,3]. The randomised versions of the analysed networks are generated using a random local rewiring algorithm that preserves the degrees of the vertices. In a rewiring step two edges (v_1, v_2) and (v_3, v_4) are rewired in such a way that v_1 becomes connected to v_4 and v_3 to v_2, provided that no such edge already exists in the network [1,3]. This rewiring step is repeated a great number of times to generate a properly randomised network. The P-value of a motif m is defined as the probability P that the frequency of m in a randomised network is equal or larger to the frequency of m in the target network [2,3].

1. Sergei Maslov and Kim Sneppen: Specificity and stability in topology of protein networks. Science, 296: 910-913, 2002.
2. Ron Milo, Shai Shen-Orr, Shalev Itzkovitz, Nadav Kashtan, Dmitri Chklovskii and Uri Alon: Network Motifs: Simple Building Blocks of Complex Networks. Science, 298: 824-827, 2002.
3. Sergei Maslov, Kim Sneppen and Uri Alon: Correlation profiles and motifs in complex networks. In: Stefan Bornholdt and Heinz-Georg Schuster, editors, Handbook of Graphs and Networks: From the Genome to the Internet. Wiley-VCH Berlin, 168-198, 2003.

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