Title: Understanding Graph Contrastive Learning From A Statistical Perspective. Abstract: Although recent advances have prompted the prosperity in graph contrastive learning, the researches on universal principles for model design and desirable properties of latent representations are still inadequate. From a statistical perspective, this paper proposes two principles for guidance and constructs a general graph self-supervised framework. Reformulating data augmentation as a mixture process, the first one, termed consistency principle, lays stress on exploring and mapping cross-view common information to consistent and essence-revealing representations. For the purpose of instantiation, four statistical indicators are employed to estimate and maximize the correlation between representations from various views, whose accordant variation trend during training implies the extraction of common content. With awareness of the insufficiency of a solo consistency principle, suffering from degenerated and coupled solutions, a decorrelation principle is put forward to encourage diverse and informative representations. Accordingly, two specific strategies, performing in representation space and eigen spectral space,  respectively, are propounded to decouple various representation channels. Under two principles, various combinations of concrete implementations derive a family of methods. Provably, after decomposition and analysis for the commonly used \textit{InfoNCE} loss, we clarify that the approaches based on mutual information maximization implicitly fulfill the two principles and are covered within our framework. The comparison experiments with current state-of-the-arts demonstrate the effectiveness and sufficiency of two principles for high-quality graph representations. Furthermore, visual studies reveal how certain principles affect learned representations.