Schroedinger-like PageRank equation and localization in the WWW

TL;DR

This paper introduces a quantum physics-inspired wave equation approach to compute PageRank efficiently, revealing how network topology influences information diffusion and page importance without iterative calculations.

Contribution

It presents a novel Schroedinger-like equation formulation for PageRank, enabling direct and faster computation and providing insights into the role of topology in web page importance.

Findings

The new method is faster than traditional iterative PageRank algorithms.

Topological disorder affects wave function localization and page scores.

The approach offers a quantum physics perspective on WWW network analysis.

Abstract

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.