Analysis of interactive narrative is a complex undertaking, requiring understanding of the narrative's design, its affordances, and its impact on players. Analysis is often performed by an expert, but this is expensive and difficult for complex interactive narratives. Automated analysis of structure, the organization of interaction elements, could help augment an expert's analysis. For this purpose we developed a model consisting of a set of metrics to analyze interactive narrative structure, enabled by a novel multi-graph representation. We implemented this model for an interactive scenario authoring tool called StudyCrafter and analyzed 20 student-designed scenarios. We show that the model illuminates the structures and groupings of the scenarios. This work provides insight for manual analysis of attributes of interactive narratives and a starting point for automated design assistance.