Meta paths are good mechanisms to improve the quality of graph analysis on heterogeneous information networks. This paper presents a meta path graph clustering framework, VEPathCluster, that combines meta path vertex-centric clustering with meta path edge-centric clustering for improving the clustering quality of heterogeneous networks. First, we propose an edge-centric path graph model to capture the meta-path dependencies between pairwise path edges. We model a heterogeneous network containing M types of meta paths as M vertex-centric path graphs and M edge-centric path graphs. Second, we propose a clustering-based multigraph model to capture the fine-grained clustering-based relationships between pairwise vertices and between pairwise path edges. We perform clustering analysis on both a unified vertex-centric path graph and each edge-centric path graph to generate vertex clustering and edge clusterings of the original heterogeneous network respectively. Third, a reinforcement algorithm is provided to tightly integrate vertex-centric clustering and edge-centric clustering by mutually enhancing each other. Finally, an iterative learning strategy is presented to dynamically refine both vertex-centric clustering and edge-centric clustering by continuously learning the contributions and adjusting the weights of different path graphs.