Alzheimer’s disease (AD) is a well-known neurodegenerative disease that is associated with dramatic morphological abnormalities. The default mode network (DMN) is one of the most frequently studied resting-state networks. However, less is known about specific structural dependency or interactions among brain regions within the DMN in AD. In this study, we performed a Bayesian network (BN) analysis based on regional grey matter volumes to identify differences in structural interactions among core DMN regions in structural MRI data from 80 AD patients and 101 normal controls (NC). Compared to NC, the structural interactions between the medial prefrontal cortex (mPFC) and other brain regions, including the left inferior parietal cortex (IPC), the left inferior temporal cortex (ITC) and the right hippocampus (HP), were significantly reduced in the AD group. In addition, the AD group showed prominent increases in structural interactions from the left ITC to the left HP, the left HP to the right ITC, the right HP to the right ITC, and the right IPC to the posterior cingulate cortex (PCC). The BN models significantly distinguished AD patients from NC with 87.12% specificity and 81.25% sensitivity. We then used the derived BN models to examine the replicability and stability of AD-associated BN models in an independent dataset and the results indicated discriminability with 83.64% specificity and 80.49% sensitivity. The results revealed that the BN analysis was effective for characterising regional structure interactions and the AD-related BN models could be considered as valid and predictive structural brain biomarker models for AD. Therefore, our study can assist in further understanding the pathological mechanism of AD, based on the view of the structural network, and may provide new insights into classification and clinical application in the study of AD in the future.