This paper focuses on two fundamental graph recognition tasks: node classification and graph classification. Existing methods usually learn the node and graph representations for these two tasks separately, and ignore modeling the relations between the local and global structures. In this paper, we propose a general approach to learn the local and global features collaboratively: (1) in order to characterize the correlation among nodes and communities (a set of nodes), we employ the joint community detection/dynamic routing modules to generate the clustering assignment matrices at first and then utilize these matrices to cluster nodes to capture the global information of graphs (locally relevant graph representations). Inspired by the success of spectral clustering, we minimize the ratiocut loss to help optimize the learned assignment matrices. (2) We maximize the mutual information between local and global representations to help learn the globally relevant node representations. Experimental results on a variety of node and graph classification benchmarks show that our model can achieve superior performance over the state-of-the-art approaches.