Graph self-supervised learning aims to acquire effective graph structural representations without manual annotations. Although graph contrastive learning (GCL) enables self-supervised training by generating label-preserving perturbed views and maximizing their similarity to the original view, existing methods predominantly adopt a globally uniform perturbation strategy, which neglects the heterogeneity of node roles in real-world networks. Such indiscriminate random corruption violates the label-invariance assumption. Empirical observations indicate that real-world networks generally exhibit a core-periphery bi-layered topological architecture: core nodes form highly interconnected information hubs, and destructive perturbations applied to them are likely to cause semantic distortion and label shifts. To address these limitations, this study proposes a core-periphery structure-aware graph contrastive learning framework, with the following innovations: (i) instead of global uniform perturbation paradigm, peripheral nodes are accurately identified via a core-periphery detection algorithm, and localized perturbations are applied to preserve the integrity of the core topology, thereby strictly satisfying the principle of label invariance; (ii) augmentation operations such as peripheral node deletion are designed to simulate the dynamic evolution of real-world networks, encouraging the model to capture topological stability and noise robustness; (iii) a core-periphery contrastive loss function is constructed, in which differentiated weights are assigned to nodes with varying structural importance during loss computation, effectively guiding the model to emphasize core information while suppressing potential negative interference from peripheral nodes. Extensive experiments on multiple benchmark datasets demonstrate that the proposed method consistently outperforms state-of-the-art models across various tasks.