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Based on a unique data set referencing exposures on single name credit default swaps (CDS) on European reference entities, we study the structure and the topology of the European CDS market and its evolution from 2008 to 2012, resorting to network analysis. The structural features revealed show bilateral CDS exposures describing growing scale-free networks whose highly interconnected hubs constitute both a strength and weakness for the stability of the system. The potential" super spreaders" of financial contagion, identified as the most interconnected participants, consist mostly of banks. For some of them net notional exposures may be particularly large relative to their total common equity. Our findings also point to the importance of some non-dealer/non-bank participants belonging to the shadow banking system.