  The WorldWide Web is one of the most important communication systems we use
in our everyday life. Despite its central role, the growth and the development
of the WWW is not controlled by any central authority. This situation has
created a huge ensemble of connections whose complexity can be fruitfully
described and quantified by network theory. One important application that
allows to sort out the information present in these connections is given by the
PageRank alghorithm. Computation of this quantity is usually made iteratively
with a large use of computational time. In this paper we show that the PageRank
can be expressed in terms of a wave function obeying a Schroedinger-like
equation. In particular the topological disorder given by the unbalance of
outgoing and ingoing links between pages, induces wave function and potential
structuring. This allows to directly localize the pages with the largest score.
Through this new representation we can now compute the PageRank without
iterative techniques. For most of the cases of interest our method is faster
than the original one. Our results also clarify the role of topology in the
diffusion of information within complex networks. The whole approach opens the
possibility to novel techniques inspired by quantum physics for the analysis of
the WWW properties.
