One of the main goals in systems biology is to learn molecular regulatory networks from quantitative profile data. In particular, Gaussian Graphical Models (GGMs) are widely used network models in bioinformatics where variables (e.g. transcripts, metabolites or proteins) are represented by nodes, and pairs of nodes are connected with an edge according to their partial correlation. Reconstructing a GGM from data is a challenging task when the sample size is smaller than the number of variables. The main challenge consists in finding the inverse of the covariance estimator which is ill-conditioned in this case. Shrinkage based covariance estimators are a popular approach, producing an invertible shrunk covariance. However, a proper significance test for the shrunk partial correlation (i.e. the GGM edges) is an open challenge as a probability density including the shrinkage is unknown. In this article we present (i) a geometric reformulation of the shrinkage based GGM, and (ii) a probability density that naturally includes the shrinkage parameter.