A visual display of the most important universities in the world is the aim of this paper. It shows the topological characteristics and describes the web relationships among universities of different countries and continents. The first 1000 higher education institutions from the Ranking Web of World Universities were selected and their link relationships were obtained from Yahoo! Search. Network graphs and geographical maps were built from the search engine data. Social network analysis techniques were used to analyse and describe the structural properties of the whole of the network and its nodes. The results show that the world-class university network is constituted from national sub-networks that merge in a central core where the principal universities of each country pull their networks toward international link relationships. The United States dominates the world network, and within Europe the British and the German sub-networks stand out.