Reconstructing commuting networks is of great significance to our society. It not only provides a means to better understand human behaviors but is also essential for mobility-related research. Although some reconstruction methods are available, a physically meaningful and predictively powerful model is still missing. To fill in this gap, a dedicated and advanced reconstruction method, utilizing a geographic competition graph (GCG) and a distance-tiered graph neural network (DtGNN), is suggested in this paper. The new GCG physically and meaningfully models the competition relationship behind the job selection process, supported by DtGNN, a dedicated GNN, which utilizes distance information to realize weights sharing and achieves node embedding for commuting flow prediction. The effectiveness of the approach is confirmed via extensive experiments on real-world data. Significant improvements are observed, as compared to both traditional/machine-learning commuting models, resulting in accurate reconstruction of commuting networks with limited partial data. Detailed analyses on the impacts of model parameters, data efficiency of the algorithm, and importance of socioeconomic indicators, have also been conducted. The results also shed light on keeping the model physically meaningful when implementing GNNs.