Insight into brain development and organization can be gained by computing correlations between structural and functional measures in parcellated cortex. Partial correlations can often reduce ambiguity in correlation data by identifying those pairs of regions whose similarity cannot be explained by the influence of other regions with which they may both interact. Consequently a graph with edges indicating non-zero partial correlations may reveal important subnetworks obscured in the correlation data. Here we describe and investigate PC*, a graph pruning algorithm for identification of the partial correlation network in comparison to direct calculation of partial correlations from the inverse of the sample correlation matrix. We show that PC* is far more robust and illustrate its use in the study of covariation in cortical thickness in ROIs defined on a parcellated cortex.