In this paper we address the manifold nature of knowledge through the analysis of four distinct but complementary phenomena (Internet hyperlinks, European research networks, EPO co-patent applications, Erasmus students mobility) that characterize knowledge as an intrinsic relational structure (directly) connecting people, institutions and (indirectly) regions across five European countries. We study the structure (in terms of density, clustering and centralisation) of these networks through network analysis techniques and test the influence of geographical distance as opposed to sectoral (based on the industrial distribution of the innovative activity) and functional (based on the value of the RSII European technological leadership index) distances in shaping the strength of knowledge relations though a gravitational model. The empirical analysis shows the existence of a polarized centre-periphery hierarchy of European regions that is reflected in the structure of knowledge flows. By using a gravitational model we demonstrate that, far from the claim of the death of distance, geographic distance is still relevant for determining the structure of inter-regional knowledge flows. Functional and sectoral distances play also a crucial role suggesting that knowledge flows easily between similar (according to their scientific, technological and sectoral characteristics) regions. If the EU intends to build a truly European Research Area in which the networking of centres of excellence acts as catalysts for backward areas this target may still be far away.