IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-06-16T08:33:21ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2014-12-10T14:41:25Z2014-12-10T14:41:25Zhttp://eprints.imtlucca.it/id/eprint/2407This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/24072014-12-10T14:41:25ZSchroedinger-like PageRank equation and localization in the WWWThe 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. Nicola PerraVinko ZlaticAlessandro Chessaalessandro.chessa@imtlucca.itClaudio ContiDebora DonatoGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-03T14:29:51Z2014-12-18T16:02:51Zhttp://eprints.imtlucca.it/id/eprint/1109This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11092012-02-03T14:29:51ZPreferential attachment in the growth of social networks: the internet encyclopedia WikipediaWe present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.Andrea CapocciVito D. P. ServedioFrancesca ColaioriLuciana BuriolDebora DonatoStefano LeonardiGuido Caldarelliguido.caldarelli@imtlucca.it2012-01-26T10:49:27Z2013-11-20T15:59:36Zhttp://eprints.imtlucca.it/id/eprint/1083This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10832012-01-26T10:49:27ZPageRank equation and localization in the WWWWe show that the PageRank in a network can be represented as the solution of a differential equation discretized over a directed graph. By exploiting a formal relationship with the time-independent SchrÃ¶dinger equation it is possible to interpret hub formation and related phenomena as a wave-like localization process in the presence of disorder and trapping potentials. The result opens new perspectives in the physics of networks with interdisciplinary connections and opens the way to the employment of various mathematical techniques to the analysis of self-organization in structured systems. Applications are envisaged in the World-Wide Web, traffic, social and biological networks.Nicola PerraVinko ZlaticAlessandro Chessaalessandro.chessa@imtlucca.itClaudio ContiDebora DonatoGuido Caldarelliguido.caldarelli@imtlucca.it2012-01-26T10:01:25Z2012-01-26T10:55:18Zhttp://eprints.imtlucca.it/id/eprint/1081This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10812012-01-26T10:01:25ZA PageRank-based preferential attachment model for the evolution of the World Wide WebWe propose a model of network growth aimed at mimicking the evolution of the World Wide Web. To this purpose, we take as a key quantity, in the network evolution, the centrality or importance of a vertex as measured by its PageRank. Using a preferential attachment rule and a rewiring procedure based on this quantity, we can reproduce most of the topological properties of the system.P. GiammatteoDebora DonatoVinko ZlaticGuido Caldarelliguido.caldarelli@imtlucca.it