We use a factor model and elastic net shrinkage to model a high-dimensional network of European credit default swap (CDS) spreads. Our empirical approach allows us to assess the joint transmission of bank and sovereign risk to the nonfinancial corporate sector. Our findings identify a sectoral clustering in the CDS network, where financial institutions are in the center and nonfinancial entities as well as sovereigns are grouped around the financial center. The network has a geographical component reflected in different patterns of real-sector risk transmission across countries. Our framework also provides dynamic estimates of risk transmission, a useful tool for systemic risk monitoring.