Before revision:  Yet, partial correlation values convey no information on the (linear) influence of the association within the entire multivariate system or, in other words, of the represented edge within the entire network. Jones and West (2005) showed that covariance can be decomposed into the weights of the paths that connect two variables within the corresponding undirected network. Here we provide a precise interpretation of path weights and show that, in the particular case of single-edge paths, this interpretation leads to a quantity we call networked partial correlation whose value depends on both the partial correlation between the intervening variables and their association with the rest of the multivariate system.
After revision:  Yet, partial correlation values convey no information on the (linear) influence of the association within the entire multivariate system , which may be crucial to discriminate functional associations from genetic interactions. To address these two shortcomings, here we propose to use the edge weight derived from the covariance decomposition over the paths of the associated gene network. We call this new quantity the networked partial correlation whose value depends on both the partial correlation between the intervening variables and their association with the rest of the multivariate system.