The post-crisis reforms of the derivatives markets have pushed central clearing as a way to reduce counterparty credit risk and increase financial stability, making central counterparties an important part of the financial system. This paper analyzes counterparty relationships within both direct (house) and client clearing in the interest rate derivatives market in the European Union. There is a growing literature on various aspects of central clearing, yet very little attention has been paid to client clearing and its implications for financial stability and contagion effects. By means of a network analysis, we show that the structure of the network, the geography and sector of risk and the relevance of various types of counterparties for the stability of the system of counterparty relationships alter significantly if we take a holistic view. Our analysis shows that big derivatives dealers are also systemic in this market, together with central counterparties.