Multi-attributed graphs, in which each node is characterized by multiple types of attributes, are ubiquitous in the real world. Detection and characterization of communities of nodes could have a significant impact on various applications. Although previous studies have attempted to tackle this task, it is still challenging due to difficulties in the integration of graph structures with multiple attributes and the presence of noises in the graphs. Therefore, in this study, we have focused on clusters of attribute values and strong correlations between communities and attribute-value clusters. The graph clustering methodology adopted in the proposed study involves Community detection, Attribute-value clustering, and deriving Relationships between communities and attribute-value clusters (CAR for short). Based on these concepts, the proposed multi-attributed graph clustering is modeled as CAR-clustering. To achieve CAR-clustering, a novel algorithm named CARNMF is developed based on non-negative matrix factorization (NMF) that can detect CAR in a cooperative manner. Results obtained from experiments using real-world datasets show that the CARNMF can detect communities and attribute-value clusters more accurately than existing comparable methods. Furthermore, clustering results obtained using the CARNMF indicate that CARNMF can successfully detect informative communities with meaningful semantic descriptions through correlations between communities and attribute-value clusters.