Dialog is a core building block of human natural language interactions. It\ncontains multi-party utterances used to convey information from one party to\nanother in a dynamic and evolving manner. The ability to compare dialogs is\nbeneficial in many real world use cases, such as conversation analytics for\ncontact center calls and virtual agent design.\n We propose a novel adaptation of the edit distance metric to the scenario of\ndialog similarity. Our approach takes into account various conversation aspects\nsuch as utterance semantics, conversation flow, and the participants. We\nevaluate this new approach and compare it to existing document similarity\nmeasures on two publicly available datasets. The results demonstrate that our\nmethod outperforms the other approaches in capturing dialog flow, and is better\naligned with the human perception of conversation similarity.\n