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Recently, knowledge graph (KG) augmented models have achieved noteworthy success on various commonsense reasoning tasks. However, KG edge (fact) sparsity and noisy edge extraction/generation often hinder models from obtaining useful knowledge to reason over. To address these issues, we propose a new KG-augmented model: Hybrid Graph Network (HGN). Unlike prior methods, HGN learns to jointly contextualize extracted and generated knowledge by reasoning over both within a unified graph structure. Given the task input context and an extracted KG subgraph, HGN is trained to generate embeddings for the subgraph's missing edges to form a "hybrid" graph, then reason over the hybrid graph while filtering out context-irrelevant edges. We demonstrate HGN's effectiveness through considerable performance gains across four commonsense reasoning benchmarks, plus a user study on edge validness and helpfulness.