In this talk, I will introduce a sparse regression approach for covariance selection under the setting of p > n. This method depends on the overall sparsity of the concentration matrix. We study the performance of this new approach under various simulation settings. We also apply the method to high dimensional microarray data for genetic network inference, where identification of hubs (genes with many connections) is of great interest. We demonstrate that our method is more powerful compared to existing methods. Finally, we prove that, under a set of suitable assumptions, the proposed estimation of partial correlations converges to the truth.