The paper presents a method for estimating high-dimensional graphs using the Lasso for neighborhood selection, which is computationally efficient and consistent for sparse graphs. The method estimates conditional independence between variables by identifying the neighborhood of each node in the graph. The Lasso-based approach is shown to be consistent for sparse high-dimensional graphs, even when the number of variables grows as a power of the number of observations. The consistency of the method relies on the choice of the penalty parameter, which must be controlled to ensure accurate estimation of the graph structure. The paper also discusses the implications of using the prediction-oracle penalty, which is inconsistent for estimation of the true model. Instead, a penalty that controls the probability of falsely connecting distinct connectivity components of the graph is used, leading to consistent estimation with exponential rates. The method is shown to be more accurate and computationally efficient than traditional forward selection MLE, especially for graphs with a large number of nodes. Numerical results demonstrate the effectiveness of the Lasso-based neighborhood selection in estimating sparse graphs.The paper presents a method for estimating high-dimensional graphs using the Lasso for neighborhood selection, which is computationally efficient and consistent for sparse graphs. The method estimates conditional independence between variables by identifying the neighborhood of each node in the graph. The Lasso-based approach is shown to be consistent for sparse high-dimensional graphs, even when the number of variables grows as a power of the number of observations. The consistency of the method relies on the choice of the penalty parameter, which must be controlled to ensure accurate estimation of the graph structure. The paper also discusses the implications of using the prediction-oracle penalty, which is inconsistent for estimation of the true model. Instead, a penalty that controls the probability of falsely connecting distinct connectivity components of the graph is used, leading to consistent estimation with exponential rates. The method is shown to be more accurate and computationally efficient than traditional forward selection MLE, especially for graphs with a large number of nodes. Numerical results demonstrate the effectiveness of the Lasso-based neighborhood selection in estimating sparse graphs.