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].
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1.
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Sergei Maslov and Kim Sneppen: Specificity and stability in topology of protein networks. Science, 296: 910-913, 2002.
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2.
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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.
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3.
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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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