Schizophrenia, as a psychiatric disorder, has recognized brain alterations both at the structural and at the functional magnetic resonance imaging level. The developing field of connectomics has attracted much attention as it allows researchers to take advantage of powerful tools of network analysis in order to study structural and functional connectivity abnormalities in schizophrenia. Many methods have been proposed to identify biomarkers in schizophrenia, focusing mainly on improving the classification performance or performing statistical comparisons between groups. However, the stability of biomarkers selection has been for long overlooked in the connectomics field. In this study, we follow a machine learning approach where the identification of biomarkers is addressed as a feature selection problem for a classification task. We perform a recursive feature elimination and support vector machines (RFE-SVM) approach to identify the most meaningful biomarkers from the structural, functional, and multi-modal connectomes of healthy controls and patients. Furthermore, the stability of the retrieved biomarkers is assessed across different subsamplings of the dataset, allowing us to identify the affected core of the pathology. Considering our technique altogether, it demonstrates a principled way to achieve both accurate and stable biomarkers while highlighting the importance of multi-modal approaches to brain pathology as they tend to reveal complementary information.