Abstract-Synthetic aperture radar (SAR) image change detection is currently a popular topic, but the existence of speckle noise renders it challenging. Making full use of the neighborhood information can reduce noise interference and improve accuracy. To this end, this study proposes a graph-guided method for SAR image change detection. First, we establish the local, nonlocal and global connections according to three types of neighboring rules. A novel heterogeneous graph is then constructed by assigning different weights to these multi-level connections. On the basic of heterogeneous graph, a composite random walk matrix (CRWM) is presented to quantify the similarity of multi-level connections. Thereafter, the heterogeneous graph shift system consisting of the multi-order CRWM is designed to aggregate the attributes of neighboring vertices along the multi-order and multi-level connections. The change measure can be implemented by comparing the output signals from the heterogeneous graph shift systems, resulting in the generation of difference image with good separability. Finally, change analysis is carried out using binary classification algorithm. Experiments conducted on six real SAR datasets confirm that the proposed M2HG method successfully strikes a balance between speckle suppression and change enhancement. This strategic balance translates into improvements in performance metrics, with OA, κ and F1 indicators surpassing those of the sub-optimal method by 0.87%, 3.34%, and 3.84%, respectively. Overall, the proposed method emerges as a promising contender for SAR image change detection tasks.