Understanding the organizational principles of human brain activity at the systems level remains a major challenge in network neuroscience. Here, we introduce a fully data-driven approach based on graph learning to extract meaningful repeating network patterns from regionally-averaged timecourses. We use the Graph Laplacian Mixture Model (GLMM), a generative model that treats functional data as a collection of signals expressed on multiple underlying graphs. By exploiting covariance between activity of brain regions, these graphs can be learned without resorting to structural information. To validate the proposed technique, we first apply it to task fMRI with a known experimental paradigm. The probability of each graph to occur at each time-point is found to be consistent with the task timing, while the spatial patterns associated to each epoch of the task are in line with previously established activation patterns using classical regression analysis. We further on apply the technique to resting state data, which leads to extracted graphs that correspond to well-known brain functional activation patterns. The GLMM allows to learn graphs entirely from the functional activity that, in practice, turn out to reveal high degrees of similarity to the structural connectome. The Default Mode Network (DMN) is always captured by the algorithm in the different tasks and resting state data. Therefore, we compare the states corresponding to this network within themselves and with structure. Overall, this method allows us to infer relevant functional brain networks without the need of structural connectome information. Moreover, we overcome the limitations of windowing the time sequences by feeding the GLMM with the whole functional signal and neglecting the focus on sub-portions of the signals.