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In this paper we analyze the topological properties of the network of the Euro Area banking market network, with the primary aim of assessing the importance of a bank in the financial system with respect to ownership and control of other credit institutions. The network displays power law distributions in both binary and weighted degree metrics indicating a robust yet fragile structure and a direct link between an increase of control diversification and a rise in the market power. Therefore while in good time the network is seemingly robust, in bad times many banks can simultaneously go into distress. This behavior paves the way for Central bank’s actions. In particular we investigate whether the Single Supervisory Mechanism introduced by the European Central Banks and based on banks’ total asset is a good proxy to quantify their systemic importance. Results indicate that not all the financial institutions with high valued total assets are systemically important but only few of them. Moreover the network structure reveals that control is highly concentrated, with few important shareholders approximately controlling a separate subset of banks. [ABSTRACT FROM AUTHOR]