We consider the task of estimating a Gaussian graphical model in the\nhigh-dimensional setting. The graphical lasso, which involves maximizing the\nGaussian log likelihood subject to an l1 penalty, is a well-studied approach\nfor this task. We begin by introducing a surprising connection between the\ngraphical lasso and hierarchical clustering: the graphical lasso in effect\nperforms a two-step procedure, in which (1) single linkage hierarchical\nclustering is performed on the variables in order to identify connected\ncomponents, and then (2) an l1-penalized log likelihood is maximized on the\nsubset of variables within each connected component. In other words, the\ngraphical lasso determines the connected components of the estimated network\nvia single linkage clustering. Unfortunately, single linkage clustering is\nknown to perform poorly in certain settings. Therefore, we propose the cluster\ngraphical lasso, which involves clustering the features using an alternative to\nsingle linkage clustering, and then performing the graphical lasso on the\nsubset of variables within each cluster. We establish model selection\nconsistency for this technique, and demonstrate its improved performance\nrelative to the graphical lasso in a simulation study, as well as in\napplications to an equities data set, a university webpage data set, and a gene\nexpression data set.\n