01-382 Jean-Pierre Eckmann, Elisha Moses
Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web (555K, postscript) Oct 17, 01
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Abstract. Beyond the information stored in pages of the World Wide Web, a type of ``meta-information'' is created when they connect to each other. This new information is a collective effect of independent users writing and linking pages, hidden from the casual individual user. Accessing it and understanding the inter-relation of connectivity and content in the WWW is a challenging problem[refs]. We demonstrate here how thematic relationships can be precisely located by looking only at the graph of hyperlinks, gleaning content and context from the Web without having to read what is in the pages. Noting that reciprocal links (co-links) between pages signal a mutual recognition of authors, we focus on triangles containing such links, since triangles indicate a transitive relation. The importance of triangles is quantified by the clustering coefficient[Watts-Strogatz] which we show is actually 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 together 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.

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