Understanding narrative text requires capturing characters' motivations, goals, and mental states. This paper proposes an Entity-based Narrative Graph (ENG) to model the internal- states of characters in a story. We explicitly model entities, their interactions and the context in which they appear, and learn rich representations for them. We experiment with different task-adaptive pre-training objectives, in-domain training, and symbolic inference to capture dependencies between different decisions in the output space. We evaluate our model on two narrative understanding tasks: predicting character mental states, and desire fulfillment, and conduct a qualitative analysis.