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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(nlog k) queries, and exactly matches the query complexity of the algorithm introduced by [Reyzin and Srivastava, 2007] forarXiv:2112.07897v2 fatcat:ejm7h5fasbhlpexubegp7hctmm