Falls among older adults represent a critical public health challenge, with approximately 37.3 million fall-related incidents reported globally each year. Early and accurate prediction of falls is essential to enable timely, proactive interventions and to reduce associated injuries and fatalities. This work introduces a graph-based machine learning framework that leverages data from the cStick, a smart assistive Internet of Medical Things (IoMT) device. Bipartite graphs are constructed to model static correlations between multivariate sensor inputs— including heart rate variability (HRV), pressure, distance, SpO2, blood sugar levels, and accelerometer readings— and fall outcomes encoded as no fall, predicted fall, or definite fall. SHAP (SHapley Additive exPlanations) values are further integrated to enhance model interpretability and to identify the most influential sensor features through feature-only graph projections. Kernel Density Estimation (KDE) plots and pairplots are used to visualize feature distributions across fall categories. The proposed framework demonstrates that Pressure and Distance exhibit the strongest correlations with fall decisions (1.000 and −0.946, respectively), providing actionable insights for risk stratification. The integration of graph-based analysis with SHAP interpretability improves both predictive accuracy and transparency, facilitating proactive interventions and enhancing the safety, autonomy, and well-being of elderly individuals in real-world assistive care settings.