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We propose a novel edge generation procedure, Community-aware Edge Generation (CEG), which controls the internal structure of communities: hub dominance and clustering coefficient. CEG is designed to be adaptable to existing graph generators. We demonstrate the effectiveness of CEG from three aspects. First, we validate that CEG generates graphs with similar internal structures to given real-world graphs. Second, we show how the parameters of CEG control the internal structure of communities. Finally, we show that CEG can generate various types of internal structures of communities by visualizing generated graphs.