The problem of discovering a structure that fits a collection of vector data is of crucial importance for a variety of applications. Such problems can be framed as Laplacian constrained Gaussian Graphical Model inference. Existing algorithms rely on the assumption that all the available observations are drawn from the same Multivariate Gaussian distribution. However, in practice it is common to find scenarios where the datasets are contaminated with a certain number of outliers. The purpose of this work is to address that problem. We propose a robust method based on Trimmed Least Squares that copes with the presence of corrupted samples. We provide statistical guarantees on the estimation error and present results on simulated data.