Atrial fibrillation is a clinical arrhythmia with multifactorial mechanisms still unresolved. Time-frequency analysis of epicardial electrograms has been investigated to study atrial fibrillation. However, deeper understanding of atrial fibrillation can be achieved if the spatial dimension can be incorporated. Unfortunately, the physical models describing the spatial relations of atrial fibrillation signals are complex and non-linear; hence, the conventional signal processing techniques to study electrograms in the joint space, time, and frequency domain are less suitable. In this study, we wish to put forward a radically different approach to analyze atrial fibrillation with a higher-level model. This approach relies on graph signal processing to represent the spatial relations between epicardial electrograms and put forward a graph-time spectral analysis for atrial fibrillation. To capture the frequency content along both the time and graph domain, we proposed the joint graph and short-time Fourier transform. The latter allows us to analyze the spatial variability of the electrogram temporal frequencies. With this technique, we have found that the spatial variation of the atrial electrograms decreases during atrial fibrillation due to the reduction of the high temporal frequencies of the atrial waves. The proposed analysis further confirms that the ventricular activity is smoother over the atrial area compared with the atrial activity. Besides using the proposed graph-time analysis to conduct a first study on atrial fibrillation, we applied it to the cancellation of ventricular activity from atrial electrograms. Experimental results on simulated and real data further corroborate the findings in this atrial fibrillation study.