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In many recommender systems, users and items are associated with attributes, and users show preferences to items. The attribute information describes users'(items') characteristics and has a wide range of applications, such as user profiling, item annotation, and feature-enhanced recommendation. As annotating user (item) attributes is a labor intensive task, the attribute values are often incomplete with many missing attribute values. Therefore, item recommendation and attribute inference have become two main tasks in these platforms. Researchers have long converged that user (item) attributes and the preference behavior are highly correlated. Some researchers proposed to leverage one kind of data for the remaining task, and showed to improve performance. Nevertheless, these models either neglected the incompleteness of user (item) attributes or regarded the correlation of the two tasks with simple models, leading to suboptimal performance of these two tasks. To this end, in this paper, we define these two tasks in an attributed user-item bipartite graph, and propose an Adaptive Graph Convolutional Network (AGCN) approach for joint item recommendation and attribute inference. The key idea of AGCN is to iteratively perform two parts: 1) Learning graph embedding parameters with previously learned approximated attribute values to facilitate two tasks; 2) Sending the approximated updated attribute values back to the attributed graph for better graph embedding learning. Therefore, AGCN could adaptively adjust the graph embedding learning parameters by incorporating both the given attributes and the estimated attribute values, in order to provide weakly supervised information to refine the two tasks. Extensive experimental results on three real-world datasets clearly show the effectiveness of the proposed model.