We use methods from network science to analyze corruption risk in a large administrative dataset of over 4 million public procurement contracts from European Union member states covering the years 2008-2016. By mapping procurement markets as bipartite networks of issuers and winners of contracts we can visualize and describe the distribution of corruption risk. We study the structure of these networks in each member state, identify their cores and find that highly centralized markets tend to have higher corruption risk. In all EU countries we analyze, corruption risk is significantly clustered. However, these risks are sometimes more prevalent in the core and sometimes in the periphery of the market, depending on the country. This suggests that the same level of corruption risk may have entirely different distributions. Our framework is both diagnostic and prescriptive: it roots out where corruption is likely to be prevalent in different markets and suggests that different anti-corruption policies are needed in different countries.