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Thus, (Q^{mathrm{rand}})s reported in Table 4 are the mean normalized modularity scores from the 100 randomly generated networks for each sub-domain with their respective variance.
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On each of the random network we have detected cluster of nodes using Infomap and computed the normalized modularity.
In order to quantify the goodness of the community partitions detected by Infomap, we use a normalized modularity score Q.
The mean normalized difference for K ′ = 400 is approximately 0.2.
(b) Mean normalized difference of CRLBs vs. burst length K ′.
In Table 4, we report the number of communities detected by Infomap on the empirical networks and the normalized modularity score Q for the empirical networks given the Infomap partitions.
These values should be compared to the normalized modularity score (Q^{mathrm{rand}}) obtained from a set of 100 randomly generated networks using the degree sequence from the empirical networks.
The mean normalized phase durations are shown in Figure 4.
We show that: although the normalized modularity is believed to be independent of the network size [ 22], dependence remains for normalized modularities in the case of enzyme networks (see Methods).
Following Parter et al. [ 6], normalized modularity is defined as (3) Q − Q rand 1 − 1 / M − Q rand.
Bars represent mean normalized surface expression.
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