Technological innovation depends on knowledge developed by scientific research. The number of citations made in patents to the scientific literature has been suggested as an indicator of this process of transfer of knowledge from science to technology. We provide an intersectoral insight into this indicator, by breaking down patent citations into a sector-to-sector matrix of knowledge flows. We then propose a method to analyze this matrix and construct various indicators of science intensity of sectors, and the pervasiveness of knowledge flows. Our results indicate that the traditional measure of the number of citations to science literature per patent captures important aspects of intersectoral knowledge flows, but that other aspects are not captured. In particular, we show that high science intensity implies that sectors are net suppliers of knowledge in the economic sector, but that science intensity does not say much about pervasiveness of either knowledge use or knowledge supply by sectors. We argue that these results are related to the specific and specialized nature of knowledge.