Person re-identification (Re-ID) aims to match the same pedestrian in a large gallery with different cameras and views. Enhancing the robustness of the extracted feature representations is a main challenge in Re-ID. Existing methods usually improve feature representation by improving model architecture, but most methods ignore the potential contextual information, which limits the effectiveness of feature representation and retrieval performance. Neighborhood information, especially the potential information of multi-order neighborhoods, can effectively enrich feature expression and improve retrieval accuracy, but this has not been fully explored in existing research. Therefore, we propose a novel model DMON-ARO that leverages latent neighborhood information to enhance both feature representation and index performance. Our approach is built on two complementary modules: Dynamic Multi-Order Neighbor Modeling (DMON) and Asymmetric Relationship Optimization (ARO). The DMON module dynamically aggregates multi-order neighbor relationships, allowing it to capture richer contextual information and enhance feature representation through adaptive neighborhood modeling. Meanwhile, ARO refines the distance matrix by optimizing query-to-gallery relationships, improving the index accuracy. Extensive experiments on three benchmark datasets demonstrate that our approach achieves performance improvements against baseline models, which illustrate the effectiveness of our model. Specifically, our model demonstrates improvements in Rank-1 accuracy and mAP. Moreover, this method can also be directly extended to other re-identification tasks.