Person re-identification (ReID) is the task of matching individuals across different camera views. Existing approaches typically employ neural networks to extract discriminative features, ranking gallery images based on their similarities to probe images. While effective, these methods are often further enhanced through re-ranking, which refines the initial retrieval results without additional training. However, current re-ranking methods mostly rely on k-nearest neighbor search to extract similar images that might have the same identity as the query, which is time-consuming with a high computation burden, limiting their applications in reality. We rethink the effect of the k-nearest neighbor search and introduce Chebyshev's Theorem-guided Graph Re-ranking (Cheb-GR) method which adopts the adaptive neighbor search guided by Chebyshev's Theorem over the k-nearest neighbor search for efficient neighbor selection. Our method leverages graph convolution operations to refine image features and achieve robust re-ranking, leading to enhanced retrieval performance. Furthermore, we provide a theoretical analysis based on Chebyshev's Inequality to elucidate the factors contributing to the strong performance of the proposed method. Our method significantly reduces the computation costs while maintaining relatively strong performance. Through extensive experiments in both general and cross-domain settings, we demonstrate the effectiveness of Cheb-GR and its potential for real-world applications. Code will be available.