In the literature (Langfelder P and Horvath S, Eigengene networks for studying relationships between co-expression modules. BMC Systems Biology 2007, 1:54 doi:10.1186/1752-0509-1-54 (link to BMC Systems Biology)) I have found that the Module Eigengenes are used in Weighted Gene Co-expression Network Analysis, instead of Weighted Gene Correlated Network Analysis. I am doing a correlated network analysis instead of a co-expressed analysis; for correlated network analysis I mean building the modules with adjacency unsigned and TOMtype as signed, which leads to modules with genes with positive and negative correlation between them. Is the Module Eigengene representative of modules in correlation networks? I couldn't find any literature or reference addressing this.

In correlated network analysis I am considering not using the Module Eigengene, because the main difference of the modules (the first component so the ME) will be that some genes are positively correlated and others negatively correlated between them. So, when I compare the ME with the clinical variable, to select the interesting modules, I will compare in which clinical variable the difference between positive and negative gene correlation is similar to the clinical variable not if the module correlates more with a clinical outcome.

When I plot the Gene Significance of a module vs the Module Membership referred to the Module Eigengene (in a correlation network analysis), I can clearly see two groups, one with positive correlation with the Module Eigengene and another with a negative Module Eigengene correlation. Thus, to select the module more correlated to a given clinical variable should I use the absolute correlation between the GS and the MM is higher in a correlated network analysis?

Weighted Gene Co-expression Network Analysis (WGCNA) is a particular application of what we call Weighted Correlation Network Analysis (which should be abbreviated to WCNA, but we use WGCNA for both). What you refer to is the difference between signed and unsigned networks.

In an unsigned network you can still use module eigengenes and kME just as you would in a signed network, but you should select hub genes based on abs(kME), not kME itself. You can use absolute value of correlation of GS and MM to select modules in both signed and unsigned networks, the procedure is the same.

In terms of literature, all early WGCNA applications (until about 2009 or 2010) were of the unsigned variety (what you call a "correlated" network).