We study the intricate relationships within healthcare systems, focusing on interactions among doctors, departments, and hospitals. Leveraging an evolutionary graph framework, the proposed model emphasizes both intra-layer and inter-layer trust relationships to better understand and optimize healthcare services. The trust-based network facilitates the identification of key healthcare entities by integrating their social and professional interactions, culminating in a trust-based algorithm that quantifies the importance of these entities. Validation with a real-world dataset reveals a strong correlation (0.91) between the proposed trust measures and the ratings of hospitals and departments, though doctor ratings demonstrate skewed distributions due to potential biases. By modeling these relationships and trust dynamics, the framework supports scalable healthcare infrastructure, enabling effective patient referrals, personalized recommendations, and enhanced decision-making pathways.