This study investigates the critical risks associated with energy transitions (ETs) affecting the energy supply chain within India's manufacturing sector. Employing the Graph Theoretic and Matrix Approach (GTMA), the research offers a structured decision-making framework that captures the interdependencies and dynamic interactions among key risk factors. GTMA facilitates a comprehensive evaluation of complex systems by identifying, modeling, and prioritizing the relative intensity of each risk component. The study proposes targeted risk mitigation strategies aimed at enhancing transparency, resilience, and efficiency throughout the transition process. The findings reveal that safety and security risks, along with political and regulatory uncertainties, emerge as the most significant barriers to effective energy transition. The outcomes contribute valuable guidance for policymakers and industry stakeholders by emphasizing the importance of robust energy governance, market-based incentives, and technological innovation in supporting a sustainable energy future for India's manufacturing sector.