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There is consensus among scholars and policy makers that knowledge is one of the key drivers of long-run economic growth. It is also clear from the literature that not all knowledge has the same value. However, too often in economic geography and cognate fields we have been obsessed with counting knowledge inputs and outputs rather than assessing the quality of knowledge produced. In this article we measure the complexity of knowledge, we map the distribution and the evolution of knowledge complexity in US cities, and we explore how the spatial diffusion of knowledge is linked to complexity. Our knowledge complexity index rests on the bimodal network models of Hidalgo and Hausmann. Analysis is based on more than two million patent records from the US Patent and Trademark Office that identify the technological structure of US metropolitan areas in terms of the patent classes in which they are most …