I am working on Gene-Gene interaction networks. I build a graph by adding edges between genes (nodes) representing statistical interaction in prediction of a quantitative parameter value (say, brain volume) in a multiple regression model.
For creating a well-connected graph, I have lowered the p-value threshold of the linear model interaction term in order to include as many edges as possible, so it is likely that a proportion of these links are false-positives (actually I have omitted multiple comparison correction and used a nominal p<0.05).
My question is that, if some nodes show a very high degree centrality which is very unlikely to happen in a random Erdős–Rényi model (aka Poisson distribution), can I make a statistical inference that this node is biologically relevant to the brain size parameter because it has "received" more than random edges, even if the whole graph does not show a Erdős–Rényi degree distribution pattern? What is the best test for statistical evaluation of this hypothesis, and if there exists one, is it also necessary to perform a multiple-comparison?