Graphs are unifying abstractions to encode, inspect and update interlinked data. They are becoming popular in several application domains with real users. In many cases, graph data is inconsistent and necessitates transformations to fix the underlying constraint violations. In this paper, we address the problem of interactive graph repairing, where users are key to the process of selecting and validating graph transformations after neighborhood constraint violations. We propose a theoretical approach to model the user involvement in the graph repair process, and we prove that minimizing the number of interactions is NP-hard. Then, we abstract away the solution space to Question-Answer-Repair (QAR) frameworks, composed of three key elements: selecting the question to be asked to the user, selecting the answer, and applying the answer as a graph repair operation. Then, we define and study the properties of termination, oracle optimality, and question difficulty to further characterize the solutions beyond the number of interactions. We evaluate our approach and the QAR frameworks on both synthetic and real-world datasets, considering different classes of users. We show that relatively high repair quality can be achieved with users that provide random answers, whereas more sophisticated users such as oracles achieve results equivalent to the ground truth.