Purpose: The main goal of this study is to investigate the discrimination power of Grey Matter (GM) thickness connectome data between Multiple Sclerosis (MS) clinical profiles using statistical and Machine Learning (ML) methods. Materials and Methods: A dataset composed of 90 MS patients acquired at the MS clinic of Lyon Neurological Hospital was used for the analysis. Four MS profiles were considered, corresponding to Clinical Isolated Syndrome (CIS), Relapsing-Remitting MS (RRMS), Secondary Progressive MS (SPMS), and Primary Progressive MS (PPMS). Each patient was classified in one of these profiles by our neurologist and underwent longitudinal MRI examinations including T1-weighted image acquisition at each examination, from which the GM tissue was segmented and the cortical GM thickness measured. Following the GM parcellation using two different atlases (FSAverage and Glasser 2016), the morphological connectome was built and six global metrics (Betweenness Centrality (BC), Assortativity (r), Transitivity (T), Efficiency (E g ), Modularity (Q) and Density (D)) were extracted. Based on their connectivity metrics, MS profiles were first statistically compared and second, classified using four different learning machines (Logistic Regression, Random Forest, Support Vector Machine and AdaBoost), combined in a higher level ensemble model by majority voting. Finally, the impact of the GM spatial resolution on the MS clinical profiles classification was analyzed. Results: Using binary comparisons between the four MS clinical profiles, statistical differences and classification performances higher than 0.7 were observed. Good performances were obtained when comparing the two early clinical forms, RRMS and PPMS (F1 score of 0.86), and the two neurodegenerative profiles, PPMS and SPMS (F1 score of 0.72). When comparing the two atlases, slightly better performances were obtained with the Glasser 2016 atlas, especially between RRMS with PPMS (F1 score of 0.83), compared to the FSAverage atlas (F1 score of 0.69). Also, the thresholding value for graph binarization was investigated suggesting more informative graph properties in the percentile range between 0.6 and 0.8. Conclusion: An automated pipeline was proposed for the classification of MS clinical profiles using six global graph metrics extracted from the GM morphological connectome of MS patients. This work demonstrated that GM morphological connectivity data could provide good classification performances by combining four simple ML models, without the cost of long and complex MR techniques, such as MR diffusion, and/or deep learning architectures.