Multi-view graph clustering aims to enhance clustering performance by integrating heterogeneous information collected in different do- mains. Each domain provides a different view of the data instances. Leveraging cross-domain information has been demonstrated an effective way to achieve better clustering results. Despite the previous success, existing multi-view graph clustering methods usually assume that different views are available for the same set of in- stances. Thus instances in different domains can be treated as having strict one-To-one relationship. In many real-life applications, however, data instances in one domain may correspond to multiple instances in another domain. Moreover, relationships between in- stances in different domains may be associated with weights based on prior (partial) knowledge. In this paper, we propose a flexible and robust framework, CGC (Co-regularized Graph Clustering), based on non-negative matrix factorization (NMF), to tackle these challenges. CGC has several advantages over the existing method- s. First, it supports many-To-many cross-domain instance relation- ship. Second, it incorporates weight on cross-domain relationship. Third, it allows partial cross-domain mapping so that graphs in different domains may have different sizes. Finally, it provides users with the extent to which the cross-domain instance relationship violates the in-domain clustering structure, and thus enables users to re-evaluate the consistency of the relationship. Extensive experimental results on UCI benchmark data sets, newsgroup data sets and biological interaction networks demonstrate the effectiveness of our approach.