Functional MRI (fMRI) research, employing naturalistic stimuli like movies, explores brain network interactions in complex cognitive processes such as empathy. The empathy network encompasses multiple brain areas, including the Insula, PFC, ACC, and parietal regions. Our novel processing pipeline applies graph learning methods to whole-brain timeseries signals, incorporating high-pass filtering, voxel-level clustering, and windowed graph learning with a sparsity-based approach. The study involves two short movies shown to 14 healthy volunteers, considering 54 regions extracted from the AAL Atlas. The sparsity-based graph learning consistently outperforms, achieving over 88% accuracy in capturing emotion contagion variations. Temporal analysis reveals a gradual induction of empathy, supported by the method's effectiveness in capturing dynamic connectomes through graph clustering. Edge-weight dynamics analysis underscores sparsity-based learning's superiority, while connectome-network analysis highlights the pivotal role of the Insula, Amygdala, and Thalamus in empathy. Spectral filtering analysis emphasizes the band-pass filter's significance in isolating regions linked to emotional and empathetic processing during empathy HIGH states. Key regions like Amygdala, Insula, and Angular Gyrus consistently activate, supporting their critical role in immediate emotional responses. Strong similarities across movies in graph cluster labels, connectome-network analysis, and spectral filtering-based analyses reveal robust neural correlates of empathy. These findings advance our understanding of empathy-related neural dynamics and identify specific regions in empathetic responses, offering insights for targeted interventions and treatments associated with empathetic processing.