Narrative similarity extends beyond standard semantic tasks, requiring alignment of temporal, causal, and emotional structures. We present StoryNet, a framework that represents stories as heterogeneous graphs with character, event, and theme nodes. Stories are decomposed into structured narrative facets using large language models, and similarity is evaluated through both weighted semantic facet comparison and a graph neural network trained with contrastive learning. We analyze how integrating symbolic structure with learned graph representations compares to purely embedding-based baselines.