Firms' innovation potential depends on their position in the R&D network. But details on this relation remain unclear because measures to quantify network embeddedness have been controversially discussed. We propose and validate a new measure, coreness, obtained from the weighted k-core decomposition of the R&D network. Using data on R&D alliances, we analyse the change of coreness for 14,000 firms over 25 years and patenting activity. A regression analysis demonstrates that coreness explains firms' R&D output by predicting future patenting.