Single-cell ATAC-seq technology advances our understanding of single-cell heterogeneity in gene regulation by enabling exploration of epigenetic landscapes and regulatory elements. However, low sequencing depth per cell leads to data sparsity and high dimensionality, limiting the characterization of gene regulatory elements. Here, we develop scAGDE, a single-cell chromatin accessibility model-based deep graph representation learning method that simultaneously learns representation and clustering through explicit modeling of data generation. Our evaluations demonstrated that scAGDE outperforms existing methods in cell segregation, key marker identification, and visualization across diverse datasets while mitigating dropout events and unveiling hidden chromatin-accessible regions. We find that scAGDE preferentially identifies enhancer-like regions and elucidates complex regulatory landscapes, pinpointing putative enhancers regulating the constitutive expression of CTLA4 and the transcriptional dynamics of CD8A in immune cells. When applied to human brain tissue, scAGDE successfully annotated cis-regulatory element-specified cell types and revealed functional diversity and regulatory mechanisms of glutamatergic neurons.