Graph data publication has been considered as an important step for data analysis and mining. Graph data, which provide knowledge on interactions among entities, can be locally generated and held by distributed data owners. These data are usually sensitive and private, because they may be related to owners’ personal activities and can be hijacked by adversaries to conduct inference attacks. Current solutions either consider private graph data as centralized contents or disregard the overlapping of graphs in distributed manners. Therefore, this work proposes a novel framework for distributed graph publication. In this framework, differential privacy is applied to justify the safety of the published contents. It includes four phases, i.e., graph combination, plan construction sharing, data perturbation, and graph reconstruction. The published graph selection is guided by one data coordinator, and each graph is perturbed carefully with the Laplace mechanism. The problem of graph selection is formulated and proven to be NP-complete. Then, a heuristic algorithm is proposed for selection. The correctness of the combined graph and the differential privacy on all edges are analyzed. This study also discusses a scenario without a data coordinator and proposes some insights into graph publication.