In this paper, we propose a reservoir computing-based and directed graph analysis pipeline. The goal of this pipeline is to define an efficient brain representation for connectivity in stroke data derived from magnetic resonance imaging. Ultimately, this representation is used within a directed graph convolutional architecture and investigated with explainable artificial intelligence (AI) tools. Stroke is one of the leading causes of mortality and morbidity worldwide, and it demands precise diagnostic tools for timely intervention and improved patient outcomes. Neuroimaging data, with their rich structural and functional information, provide a fertile ground for biomarker discovery. However, the complexity and variability of information flow in the brain requires advanced analysis, especially if we consider the case of disrupted networks as those given by the brain connectome of stroke patients. To address the needs given by this complex scenario we proposed an end-to-end pipeline. This pipeline begins with reservoir computing causality, to define effective connectivity of the brain. This allows directed graph network representations which have not been fully investigated so far by graph convolutional network classifiers. Indeed, the pipeline subsequently incorporates a classification module to categorize the effective connectivity (directed graphs) of brain networks of patients versus matched healthy control. The classification led to an area under the curve of 0.69 with the given heterogeneous dataset. Thanks to explainable tools, an interpretation of disrupted networks across the brain networks was possible. This elucidates the effective connectivity biomarker's contribution to stroke classification, fostering insights into disease mechanisms and treatment responses. This transparent analytical framework not only enhances clinical interpretability but also instills confidence in decision-making processes, crucial for translating research findings into clinical practice. Our proposed machine learning pipeline showcases the potential of reservoir computing to define causality and therefore directed graph networks, which can in turn be used in a directed graph classifier and explainable analysis of neuroimaging data. This complex analysis aims at improving stroke patient stratification, and can potentially be used with other brain diseases.