Task-oriented dialogue systems typically rely on large amounts of high-quality training data or require complex handcrafted rules. However, existing datasets are often limited in size con- sidering the complexity of the dialogues. Additionally, conventional training signal in- ference is not suitable for non-deterministic agent behavior, namely, considering multiple actions as valid in identical dialogue states. We propose the Conversation Graph (ConvGraph), a graph-based representation of dialogues that can be exploited for data augmentation, multi- reference training and evaluation of non- deterministic agents. ConvGraph generates novel dialogue paths to augment data volume and diversity. Intrinsic and extrinsic evaluation across three datasets shows that data augmentation and/or multi-reference training with ConvGraph can improve dialogue success rates by up to 6.4%.