Social relationship mining is a hot topic in the area of massive graph analysis. Graph clustering algorithms such as SCAN (structural clustering algorithm for networks) can quickly discover the communities from the massive graph data. However, relationships in these communities fail to reflect the ‘real’ social information such as family, colleagues and classmates. In reality, social data is very complex, and there are many types of interaction among each individual, such as calling, meeting, chatting in WeChat, and sending emails. However, traditional SCAN algorithm can only handle single dimensional graph data. Based on the study of multidimensional social graph data and traditional clustering algorithms, this paper first proposes an efficient subspace clustering algorithm named SCA by mining multi-dimensional clusters in subspaces as a mean to explore real social relationships. SCA follows the bottom-up principle and can discover the set of clusters from the social graph data in all dimensions. To improve the efficiency of SCA, the paper also develops a pruning algorithm called SCA+ based on the monotonicity of subspace clustering. Extensive experiments on several real-world multi-dimensional graph data demonstrate the efficiency and effectiveness of the proposed algorithms.