Network analysis: edges and statistical significance
I'm new to network analysis, and I would like to ask a doubt about edges and what they mean. From what I have understood reading articles and tutorials related to network analysis, the presence of an edge between two nodes means that a covariance exists between the two variables represented by those nodes. When we apply some regularization processes (e.g., EBICglasso), we select parameters to set the "level" of edge shrinkage, and edges are calculated like partial correlations.
Does it mean that these associations are statistically significant, as if they were considered as partial correlations with p<0.05? Or maybe the concept of statistical significance does not fully apply here?