This study uses a graph-based approach to analyse the brain MRI data of early-stage Borderline Personality Disorder (BPD) patients. The topological properties of their Functional Connectivity and Structural Covariance weighted networks are explored. Compared to healthy controls, BPDs exhibit statistically significant alterations at global level, in terms of efficiency and modularity, and at local level, in centrality and efficiency, especially from the functional perspective. The nodal variations are mostly observed in the limbic system, in particular in those regions associated to emotion regulation. Such results may be anticipating structural alterations emerging in later stages of the disease.