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Novel class discovery (NCD) aims to infer novel categories in an unlabeled dataset leveraging prior knowledge of a labeled set comprising disjoint but related classes. Existing research focuses primarily on utilizing the labeled set at the methodological level, with less emphasis on the analysis of the labeled set itself. Thus, in this paper, we rethink novel class discovery from the labeled set and focus on two core questions: (i) Given a specific unlabeled set, what kind of labeled set can best support novel class discovery? (ii) A fundamental premise of NCD is that the labeled set must be related to the unlabeled set, but how can we measure this relation? For (i), we propose and substantiate the hypothesis that NCD could benefit more from a labeled set with a large degree of semantic similarity to the unlabeled set. Specifically, we establish an extensive and large-scale benchmark with varying degrees of semantic similarity between labeled/unlabeled datasets on ImageNet by leveraging its hierarchical class structure. As a sharp contrast, the existing NCD benchmarks are developed based on labeled sets with different number of categories and images, and completely ignore the semantic relation. For (ii), we introduce a mathematical definition for quantifying the semantic similarity between labeled and unlabeled sets. In addition, we use this metric to confirm the validity of our proposed benchmark and demonstrate that it highly correlates with NCD performance. Furthermore, without quantitative analysis, previous works commonly believe that label information is always beneficial. However, counterintuitively, our experimental results show that using labels may lead to sub-optimal outcomes in low-similarity settings.