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Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for n≥k≥2, learning the components of an n-vertex hidden graph with k components requires at least (k−1)n−(k2) membership queries. Our result improves on the best known information-theoretic bound of Ω(nlogk) queries, and exactly matches the query complexity of the algorithm introduced by [Reyzin and Srivastava, 2007] for this problem. Additionally, we introduce an oracle that can learn the number of components of G in asymptotically fewer queries than learning the full partition, thus answering another question posed by the same authors. Lastly, we introduce a more applicable version of this oracle, and prove asymptotically tight bounds of ˜Θ(m) queries for both learning and verifying an m-edge hidden graph G using it.