Despite the rapid advancements of electrocardiogram (ECG) signal diagnosis and analysis methods through deep learning, two major hurdles still limit their clinical adoption: the lack of versatility in processing ECG signals with diverse configurations, and the inadequate detection of risk signals due to sample imbalances. Addressing these challenges, we introduce VersAtile and Risk-Sensitive cardiac diagnosis (VARS), an innovative approach that employs a graph-based representation to uniformly model heterogeneous ECG signals. VARS stands out by transforming ECG signals into versatile graph structures that capture critical diagnostic features, irrespective of signal diversity in the lead count, sampling frequency, and duration. This graph-centric formulation also enhances diagnostic sensitivity, enabling precise localization and identification of abnormal ECG patterns that often elude standard analysis methods. To facilitate representation transformation, our approach integrates denoising reconstruction with contrastive learning to preserve raw ECG information while highlighting pathognomonic patterns. We rigorously evaluate the efficacy of VARS on three distinct ECG datasets, encompassing a range of structural variations. The results demonstrate that VARS not only consistently surpasses existing state-of-the-art models across all these datasets but also exhibits substantial improvement in identifying risk signals. Additionally, VARS offers interpretability by pinpointing the exact waveforms that lead to specific model outputs, thereby assisting clinicians in making informed decisions. These findings suggest that our VARS will likely emerge as an invaluable tool for comprehensive cardiac health assessment.