The importance of the knowledge-base in regional and urban competition is generally recognised, although causal relations between urban and regional economic growth and knowledge level are far from clear. This paper presents the first analysis of the strength, interrelations and nodality of the global research centres. The data are records in the Science Catation Index 1997-99 of papers produced by authors from the 40 largest `greater' urban regions of the world as measured by research output. The network of research co-operation depends on nationality, distance and other factors. The top-level nodes in the co-operation network of the world are London, Geneve-Lausanne and the San Francisco Bay Area. In absolute number of co-authored papers, Los Angeles, Boston and New York constitute a second level and, when observed links are related to expected links, the second level combines Amsterdam-Hague-Rotterdam-Utrecht, Paris, Basel-Mulhouse-Freiburg and Copenhagen-Lund. As expected, the networks of citation are, by contrast, very independent of distance, but not of nationality. The primary categories of research centres for the total number of citings presented are San Diego, Seattle, Boston, New York and the San Francisco Bay Area. When we turn to the international data-set, it is Mannheim-Heidelberg, Geneve-Lausanne, Basel-Mulhouse-Freiburg and Cambridge which are in the lead.