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Self-supervised pre-training is gaining increasingly more popularity in AI-aided drug discovery, leading to more and more pre-trained models with the promise that they can extract better feature representations for molecules. Yet, the quality of learned representations have not been fully explored. In this work, inspired by the two phenomena of Activity Cliffs (ACs) and Scaffold Hopping (SH) in traditional Quantitative Structure-Activity Relationship (QSAR) analysis, we propose a method named Representation-Property Relationship Analysis (RePRA) to evaluate the quality of the representations extracted by the pre-trained model and visualize the relationship between the representations and properties. The concepts of ACs and SH are generalized from the structure-activity context to the representation-property context, and the underlying principles of RePRA are analyzed theoretically. Two scores are designed to measure the generalized ACs and SH detected by RePRA, and therefore the quality of representations can be evaluated. In experiments, representations of molecules from 10 target tasks generated by 7 pre-trained models are analyzed. The results indicate that the state-of-the-art pre-trained models can overcome some shortcomings of canonical Extended-Connectivity FingerPrints (ECFP), while the correlation between the basis of the representation space and specific molecular substructures are not explicit. Thus, some representations could be even worse than the canonical fingerprints. Our method enables researchers to evaluate the quality of molecular representations generated by their proposed self-supervised pre-trained models. And our findings can guide the community to develop better pre-training techniques to regularize the occurrence of ACs and SH.