Conversational Machine Reading (CMR) aims at answering questions in complicated interactive scenarios. Machine needs to answer questions through interactions with users based on given rule document, user scenario and dialogue history, and even initiatively asks questions for clarification if necessary. Namely, the answer to the task needs a machine in the response of either Yes, No, Irrelevant or to raise a follow-up question for further clarification. To effectively capture multiple objects in such a challenging task, graph modeling is supposed to be adopted, though it is surprising that this does not happen until this work proposes a dialogue graph modeling framework by incorporating two complementary graph models, i.e., explicit discourse graph and implicit discourse graph, which respectively capture explicit and implicit interactions hidden in the rule documents. The proposed model is evaluated on the ShARC benchmark and achieves new state-of-the-art by first exceeding the milestone accuracy score of 80%.