Story timeline summarization is widely used by analysts, law enforcement agencies, and policymakers for content presentation, story-telling, and other data-driven decision-making applications. Recent advancements in web technologies have rendered social media sites such as Twitter and Facebook as a viable platform for discovering evolving stories and trending events for story timeline summarization. However, a timeline summarization structure that models complex evolving stories by tracking event evolution to identify different themes of a story and generate a coherent structure that is easy for users to understand is yet to be explored. In this paper, we propose StoryGraph, a novel graph timeline summarization structure that is capable of identifying the different themes of a story. By using high penalty metrics that leverage user network communities, temporal proximity, and the semantic context of the events, we construct coherent paths and generate structural timeline summaries to tell the story of how events evolve over time. We performed experiments on real-world datasets to show the prowess of StoryGraph. StoryGraph outperforms existing models and produces accurate timeline summarizations. As a key finding, we discover that user network communities increase coherence leading to the generation of consistent summary structures.