A broad class of data, ranging from similarity networks, workflow networks to protein networks, can be modeled as graphs with data values as vertex labels. The vertex labels (data values) are often dirty for various reasons such as typos or erroneous reporting of results in scientific experiments. Neighborhood constraints, specifying label pairs that are allowed to appear on adjacent vertexes in the graph, are employed to detect and repair erroneous vertex labels. In this paper, we study the problem of repairing vertex labels to make graphs satisfy neighborhood constraints. Unfortunately, the relabeling problem is proved to be NP-hard, which motivates us to devise approximation methods for repairing, and identify interesting special cases (star and clique constraints) that can be efficiently solved. We propose several approximate repairing algorithms including greedy heuristics, contraction method and a hybrid approach. The performances of algorithms are also analyzed for the special case. Our extensive experimental evaluation, on both synthetic and real data, demonstrates the effectiveness of eliminating frauds in several types of application networks. Remarkably, the hybrid method performs well in practice, i.e., guarantees termination, while achieving high effectiveness at the same time.