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We study the problem of actively learning the vertex labels of a graph, assuming the classes form geodesically convex subgraphs, which is related to linear separability in the Euclidean setting. The main result of this paper is a novel query-efficient active learning algorithm with label-independent upper bounds on the number of queries needed to learn all labels. For that, we use shortest path covers and provide a logarithmic approximation for the sub-problem of computing a shortest path coverdoi:10.34726/3467 fatcat:ohnnuq4egjghdlrwxazg6cxsie