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Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature inference. Prior work on local graph clustering mostly falls into two categories with numerical and combinatorial roots respectively. In this work, we draw inspiration from both fields and propose a family of convex optimization formulations based on the idea ofarXiv:2005.09810v3 fatcat:ulsu5io6j5gmjijb463b6w5ixe