Freshwater scarcity motivates membranes that simultaneously deliver high water flux and near‑complete salt rejection. Here we use all‑atom molecular dynamics (MD) to investigate pressure‑driven desalination across monolayer graphene containing sub‑nanometer pores with controlled edge chemistry. We systematically vary pore diameter (0.5–1.0 nm), geometry, and functionalization (H, OH, COOH) to map the flux–selectivity trade‑off and identify design windows for optimal performance. Simulations of saline feed solutions (monovalent and divalent salts) quantify water permeability from steady‑state volumetric flux and ion rejection from translocation statistics. Free‑energy profiles (potential of mean force) and hydration analyses reveal the mechanisms governing selectivity: ions experience a large dehydration penalty at constrictions, which is modulated by edge polarity and charge; in contrast, water benefits from low interfacial friction and the atomically thin transport length of graphene. We find that pores near the dehydration threshold (~0.7–0.9 nm) with mild polar functionalization maximize selectivity while maintaining high throughput, whereas strongly charged edges enhance ion exclusion but reduce flux due to increased water structuring. Mechanical responses under transmembrane pressure confirm pore stability within the operating range. The results provide quantitative guidelines for tailoring pore size and chemistry to achieve near‑complete salt rejection with high permeability, and they clarify when graphene outperforms thicker polymeric membranes. These insights support the rational design of next‑generation, two‑dimensional desalination membranes and suggest experimental targets for scalable fabrication.