13. The system of claim 12 , wherein the operator comprises Common Vertices, which is a function, f(u 1 ,u 2 ), that provides a number of web documents that have a link to both web documents u 1 and u 2 .
12. The system of claim 10 , further comprising: one or more web graph machines having stored thereon a web graph, the one or more web graph machines coupled with the search engine, wherein the web graph contains a plurality of interlinked web documents each represented by a node (u 1 , u 2 , . . . u n ); and wherein the search engine retrieves values of one or more operators from the one or more web graph machines based on the relative linking within the web graph of the one or more organic search results, the plurality of sponsored search results, and any of the plurality of web documents, each of which corresponds to a node in the web graph.