Multi-graph multi-label learning (MGML) represents each object as a bag-of-graphs with multiple labels, but demands large-scale labeled data whose acquisition is often difficult and costly. Self-supervised contrastive learning (SCL) mitigates label dependence by leveraging data augmentation to construct discriminative pretext tasks, proving effective for multi-instance learning. However, when applied to MGML, SCL faces two key challenges: (1) it distinguishes individual instances by their differences, whereas MGML requires modeling label correlations; (2) it assumes semantic invariance under augmentation, but structural perturbations in MGML alter label semantics. To tackle these challenges, we propose a self-suPervised contrastive rE-learning framework for mulTi-grAph multi-labeL classification (PETAL). Specifically, to model label correlations, we first define a unified label space to learn label prototypes and align features with them, yielding prototype-aligned representations. We then design a multi-granularity contrastive loss over these representations, which captures label dependencies by contrasting at the bag level, graph level, and bag-graph level. Moreover, to ensure semantic invariance, we develop a contrastive re-learning strategy based on prototype-aligned representations to generate augmentation-free positive samples. This guarantees consistent multi-label distributions without structural perturbations. Experiments on six datasets demonstrate that PETAL achieves an average improvement of 4.12\% over state-of-the-art self-supervised and supervised baselines.