Beyond the information stored in pages of the World Wide Web, novel types of
``meta-information'' are created when they connect to each other. This
information is a collective effect of independent users writing and linking
pages, hidden from the casual user. Accessing it and understanding the
inter-relation of connectivity and content in the WWW is a challenging problem.
We demonstrate here how thematic relationships can be located precisely by
looking only at the graph of hyperlinks, gleaning content and context from the
Web without having to read what is in the pages. We begin by noting that
reciprocal links (co-links) between pages signal a mutual recognition of
authors, and then focus on triangles containing such links, since triangles
indicate a transitive relation. The importance of triangles is quantified by
the clustering coefficient (Watts) which we interpret as a curvature
(Gromov,Bridson-Haefliger). This defines a Web-landscape whose connected
regions of high curvature characterize a common topic. We show experimentally
that reciprocity and curvature, when combined, accurately capture this
meta-information for a wide variety of topics. As an example of future
directions we analyze the neural network of C. elegans (White, Wood), using the
same methods.Comment: 8 pages, 5 figures, expanded version of earlier submission with more
example