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A growing body of research in the past decade has revealed that functional interaction between brain regions entail subject-specific idiosyncrasies that are highly replicable. As such, functional connectivity patterns can be seen as an individual's brain fingerprint, enabling their identification within a population, in health and disease. The conventional method involves constructing the functional connectome by treating brain regions as vertices and utilizing pairwise measures of statistical dependence, such as Pearson's correlation coefficient, between the regional time-courses as edge weights. However, by focusing on EEG data in our study, we propose an alternative approach to learn a sparse graph structure from an individual's EEG data using principles from graph signal processing. The inferred subject-specific graphs encode subtle instantaneous spatial relations between the ensemble set of EEG electrodes in such way that EEG maps are seen as smooth functions residing on the graph. We validated the inferred graphs on two publicly available EEG datasets, demonstrating that the learned graphs outperform correlation-based functional connectomes in fingerprinting performance. This talk provides an overview of our proposed method and related results, which was presented at the 2023 European Signal Processing Conference in Helsinki, Finland. The work was selected as the second-best student paper; aside from the talk, a poster was presented as part of the contest, segments of which can be found as figures in the present article.