Constrained clustering has been well-studied in the unsupervised learning society. However, how to encode constraints into community structure detection, within complex networks, remains a challenging problem. In this paper, we propose a semi-supervised learning framework for community structure detection. This framework implicitly encodes the must-link and cannot-link constraints by modifying the adjacency matrix of network, which can also be regarded as de-noising the consensus matrix of community structures. Our proposed method gives consideration to both the topology and the functions (background information) of complex network, which enhances the interpretability of the results. The comparisons performed on both the synthetic benchmarks and the real-world networks show that the proposed framework can significantly improve the community detection performance with few constraints, which makes it an attractive methodology in the analysis of complex networks.