Mental health crises such as depression and anxiety do not occur in isolation; they are shaped by the structural properties of the social networks in which individuals are embedded. While prior studies document the spread of negative emotions through emotional contagion and highlight the buffering role of social support, little is known about how different network topologies influence resilience against widespread distress. This gap is critical because understanding the structural determinants of resilience can guide interventions that strengthen community mental health. In this paper, we introduce a network-science-based simulation framework that models negative affect as a contagion process and social support as a buffering mechanism. Using the Susceptible–Infected–Susceptible (SIS) model, we systematically compare canonical topologies—Erdös–Rényi (ER), Watts–Strogatz (WS), Barabási–Albert (BA), and modular networks—across resilience metrics including peak distress, recovery time, and systemic vulnerability. Results show that clustered and modular structures buffer contagion more effectively, while scale-free networks are highly fragile under hub-targeted stress. Our findings advance the design of resilient social systems by identifying structural features that promote recovery and contain cascades of mental distress.