The cross-modal person re-identification task aims to match visible and infrared images of the same individual. The main challenges in this field arise from significant modality differences between individuals and the lack of high-quality cross-modal correspondence methods. Existing approaches often attempt to establish modality correspondence by extracting shared features across different modalities. However, these methods tend to focus on local information extraction and fail to fully leverage the global identity information in the cross-modal features, resulting in limited correspondence accuracy and suboptimal matching performance. To address this issue, we propose a quadratic graph matching method designed to overcome the challenges posed by modality differences through precise cross-modal relationship alignment. This method transforms the cross-modal correspondence problem into a graph matching task and minimizes the matching cost using a center search mechanism. Building on this approach, we further design a block reasoning module to uncover latent relationships between person identities and optimize the modality correspondence results. The block strategy not only improves the efficiency of updating gallery images but also enhances matching accuracy while reducing computational load. Experimental results demonstrate that our proposed method outperforms the state-of-the-art methods on the SYSU-MM01, RegDB, and RGBNT201 datasets, achieving excellent matching accuracy and robustness, thereby validating its effectiveness in cross-modal person re-identification.