Task-oriented dialogue systems rely on predefined conversation schemes (dialogue flows) often represented as directed acyclic graphs. These flows can be manually designed or automatically generated from previously recorded conversations. Due to variations in domain expertise or reliance on different sets of prior conversations, these dialogue flows can manifest in significantly different graph structures. Despite their importance, there is no standard method for evaluating the quality of dialogue flows. We introduce FuDGE (Fuzzy Dialogue-Graph Edit Distance), a novel metric that evaluates dialogue flows by assessing their structural complexity and representational coverage of the conversation data. FuDGE measures how well individual conversations align with a flow and, consequently, how well a set of conversations is represented by the flow overall. Through extensive experiments on manually configured flows and flows generated by automated techniques, we demonstrate the effectiveness of FuDGE and its evaluation framework. By standardizing and optimizing dialogue flows, FuDGE enables conversational designers and automated techniques to achieve higher levels of efficiency and automation.