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(a) 3 views of a complex network generated from fMRI data from one subject, before (left) and after (right) Ayahuasca ingestion (mean node degree 〈k〉 = 30).
More information about most of the methods used here can be found in refs 4, 53, 54. Figure 1 shows the networks generated from one subject before and after Ayahuasca intake, for one specific choice of mean node degree.
The node degree (i.e., number of neighbors) of each node is close to the mean node degree of the network.
The instantaneous node degree is then defined as the number of simultaneous valid single-hop receptions of the same message, and finally the mean node degree is computed analytically in both AWGN and block-fading channels.
Thus, the real-world networks fulfill the prediction of constant mean node degree.
However, for the sample of networks used here, as noted above, the mean node degree 〈k〉i is approximately constant.
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Consistent with a previous study [ 3] we found that the mean node degrees of proteins in the HTP network were generally much higher than for HC and SI networks (supplementary Fig S2a,b online), pointing to the possibility of false positives in the HTP network and possible physical constraints on the number of partners in SI networks.
By extension, the average node degree is the mean degree of all nodes.
For example, while average "real" prediction performance of GO groups is high when using protein interactions (mean AUC 0.7), the node degree ranking mean AUC is 0.63 – far above the 0.5 expected by chance.
After aggregation, this matrix exhibits high performance (mean AUC = 0.70) and modest node degree bias (mean AUC = 0.55).
As we can appreciate in Figure 4, the genes that have evidence of extreme genetic differentiation have lower values of Eccentricity and higher Node Degree mean.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com