19. The system of claim 16 , 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.
19. The system of claim 16 , 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. 24. The system of claim 19 , wherein the re-ranking engine: calculates a FunctionScore(f,u) between each of a possible pair of nodes within the plurality of sponsored search results (S) and the one or more organic search results (O), and the value of each operator (f), wherein the FunctionScore comprises 
 Σ((f(u,o)×RankWeightOrganic)/(1+log(pos(o))))/|O|, for each o in O+Σ((f(u,s)×RankWeightSponsored)/(1+log(pos(s))))/|S|, for each s in S, wherein RankWeightOrganic and RankWeightSponsored comprise normalizing weights applied to the organic and sponsored search results, respectively, and wherein pos(o) and pos(s) comprise the ranking of each organic and sponsored search result, respectively.