Health-oriented digital innovations including Patient Remote Monitoring and Virtual Healthcare Consultations have dramatically improved access to care, treatment continuity, and healthcare system responsiveness. However, these technological solutions continue to encounter persistent obstacles regarding performance enhancement, automated quality assurance processes, and operational expansion capabilities. This research presents a theoretical framework based on graph theory for analyzing and enhancing digital healthcare workflow systems. By conceptualizing system elements as graph nodes and information flows as connecting edges, our methodology identifies efficiency constraints, tests system behavior under failure conditions, and enhances data transmission pathways. Experimental findings show a 29% improvement in response time (decreasing from 120 ms to 85 ms) and a 50% enhancement in data processing capacity (increasing from 50 Mbps to 75 Mbps), confirming the effectiveness of graph-oriented optimization approaches. These enhancements support the creation of more resilient, fault-resistant, and accessible telehealth frameworks, especially in environments characterized by high demand or limited resources. The framework we propose establishes a foundation for subsequent incorporation of sophisticated technologies including artificial intelligence and distributed ledger systems into flexible and scalable digital healthcare infrastructure.