Recent U.S. and European regulations promote centrally clearing derivatives to reduce complexity and systemic risk in the financial system. With a network model, we show that their effectiveness depends on clearing patterns. More clearing does not guarantee less systemic risk. Systemic risk can increase if multilateral netting increases at the expense of bilateral netting. We study confidential derivatives regulatory data and find evidence that contagion is less likely to start in the core but more likely to spread from the core. We introduce concepts of complexity and centrality within the financial network, exploring their implications for stability and regulatory oversight.