The paper uses a graph model to examine the effects of financial market regulations on systemic risk. Focusing on central clearing, we model the financial system as a multigraph of trade and risk relations among banks. We then study the impact of central clearing by a priori estimates in the model, stylized case studies, and a simulation case study. These case studies identify the drivers of regulatory policies on risk reduction at the firm and systemic levels. The analysis shows that the effect of central clearing on systemic risk is ambiguous, with potential positive and negative outcomes, depending on the credit quality of the clearing house, netting benefits and losses, and concentration risks. These computational findings align with empirical studies, yet do not require intensive collection of proprietary data. In addition, our approach enables us to disentangle various competing effects. The approach thus provides policymakers and market practitioners with tools to study the impact of a regulation at each level, enabling decision-makers to anticipate and evaluate the potential impact of regulatory interventions in various scenarios before their implementation.