Ranking pages and the topology of the web

This paper presents our studies on the rearrangement of links in the structure of websites for the purpose of improving the valuation of a page or group of pages as established by a ranking function as Google’s PageRank. We build our topological taxonomy starting from unidirectional and bidirectional rooted trees, and up to more complex hierarchical structures as cyclical rooted trees (obtained by closing cycles on bidirectional trees) and PR–digraph rooted trees (digraphs whose condensation digraph is a rooted tree that behave like cyclical rooted trees). We give different modifications on the structure of these trees and its effect on the valuation given by the PageRank function. We derive closed formulas for the PageRank of the root of various types of trees, and establish a hierarchy of these topologies in terms of PageRank.