I believe it is not the condition but the number of replicates that are required for running WGCNA. Typically, you are required to have more than 15 samples. Ideally, I would recommend more than 30 replicates for each condition.

Here is the list of frequently asked questions: https://horvath.genetics.ucla.edu/html/CoexpressionNetwork/Rpackages/WGCNA/faq.html

Another advice would be plotting PCA/MDS plots to check if there are no Batch Effects or technical effects such as sex, non-biologicals effects.

Good luck!

I posted this as an answer outside of Biostars:

There is no correct or incorrect answer to this. To me, it makes more sense to perform WGCNA separately, so, one network for disease and one network for control:

Analysis 1:

1. generate network in Control
2. identify modules and hub genes
3. perform gene enrichment on the genes in each module

Analysis 2:

1. generate network in Disease
2. identify modules and hub genes
3. perform gene enrichment on the genes in each module

Analysis 3:

1. discuss differences between hub genes between Disease network and Control network
2. discuss differences between modules (and their gene enrichments) between Disease network and Control network

If you generate a single network for all samples (Disease + Control), then, after you identify modules, you can still try this: perform a linear regression between DiseaseStatus and the module eigenvalues:

  summary(lm(BlueModule ~ DiseaseStatus))
  summary(lm(RedModule ~ DiseaseStatus))
  summary(lm(YellowModule ~ DiseaseStatus))
  *et cetera*

Then, in this way, you would focus on the modules from which the regression produces p<0.05, as these modules may contain information about DiseaseStatus.

Kevin