Real-time collaborative graph editing system is one of the most important branches of collaborative interactive applications in the mobile platform. In a graphical editing system, there are certain constraints and associations between different graphic objects. However, the traditional consistency maintenance algorithm is mainly conducted in the linear document with unconstrained relationships, and only supports three basic operations (Insert, Delete, Update). Based on basic operations (Create, Delete, Update) supported by traditional operation transformation algorithms, this paper extends some operations (Move, Relate, Relieve) which can represent the linkage effect on the location property of graph objects. And the relationship between objects is mapped to the associated graph document model. According to types of concurrent conflict generated by different operation types under the non-linear model, some reasonable conflict solutions are designed to maintain consistency of the shared graphical document under real-time collaborative editing. Besides, when a graphical editing system containing multiple operations types is applied to the mobile platform, the existing optimistic concurrency control algorithm based on stable networks may be not applicable to the new scenario because of the instability of the mobile networks. In view of the characteristics of signal instability in mobile network environment, the traditional OT control algorithm is improved in this paper and new concurrency control is also introduced. Based on the mechanism of sending the re-transmission request for lost operations on the client site and processing it on the server side, the concurrent control algorithm in the mobile platform of unstable network has been designed. The paper develops a mobile collaborative graphics editing system named as Co-Paint, and some simulation test further verify the correctness and feasibility of the above control algorithm and conversion functions.