Synthetic aperture radar (SAR) image change detection is a challenging task due to inherent speckle noise, imbalanced class occurrence and the requirement for discriminative feature learning. The traditional handcrafted feature extraction and current convolution-based deep learning techniques have some advantages, but suffer from being limited to neighborhood-based spatial information. The nonlocally observable imbalance phenomenon that exists naturally in small area change detection has presented a huge challenge to methods that focus on local features only. In this paper, an unsupervised method based on a variational graph auto-encoder (VGAE) network was developed for object-based small area change detection using SAR images, with the advantages of alleviating the negative impact of class imbalance and suppressing speckle noise. The main steps include: 1) Three types of difference image (DI) are combined to establish a three-channel fused DI (TCFDI), which lays the data-level foundation for subsequent analysis. 2) Simple linear iterative clustering (SLIC) is used to divide the TCFDI into superpixels regarded as nodes. Two functions are proposed and developed to measure the similarity between nodes to build a weighted undirected graph. 3) A VGAE network is designed and trained using the graph and nodes, and high-level nonlocal feature representations of each node are extracted. The network, with a Gaussian Radial Basis Function constrained by geospatial distances, establishes the connection among nonlocal, but similar superpixels in the process of feature learning, which leads to speckle noise suppression and distinguishable features learned in latent space. The nodes are then identified as changed or unchanged classes via k-means clustering. Five real SAR datasets were used in comparative experiments. Up to 99.72% accuracy was achieved, which is superior to state-of-the-art methods that pay attention only to local information, thus, demonstrating the effectiveness and robustness of the proposed approach.