A stochastic model for the evolution of the web allowing link deletion

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. We present a generalisation of the basic model by allowing deletion of individual links and show that it also gives rise to a power-law distribution. We derive the mean-field equations for this stochastic model and show that by examining a snapshot of the distribution at the steady state of the model, we are able to tell whether any link deletion has taken place and estimate the link deletion probability. Our model enables us to gain some insight into the distribution of inlinks in the web graph, in particular it suggests a power-law exponent of approximately 2.15 rather than the widely published exponent of 2.1

A Study on Ranking Method in Retrieving Web Pages Based on Content and Link Analysis: Combination of Fourier Domain Scoring and Pagerank Scoring

Ranking module is an important component of search process which sorts through relevant pages. Since collection of Web pages has additional information inherent in the hyperlink structure of the Web, it can be represented as link score and then combined with the usual information retrieval techniques of content score. In this paper we report our studies about ranking score of Web pages combined from link analysis, PageRank Scoring, and content analysis, Fourier Domain Scoring. Our experiments use collection of Web pages relate to Statistic subject from Wikipedia with objectives to check correctness and performance evaluation of combination ranking method. Evaluation of PageRank Scoring show that the highest score does not always relate to Statistic. Since the links within Wikipedia articles exists so that users are always one click away from more information on any point that has a link attached, it it possible that unrelated topics to Statistic are most likely frequently mentioned in the collection. While the combination method show link score which is given proportional weight to content score of Web pages does effect the retrieval results

Random Surfing Without Teleportation

In the standard Random Surfer Model, the teleportation matrix is necessary to ensure that the final PageRank vector is well-defined. The introduction of this matrix, however, results in serious problems and imposes fundamental limitations to the quality of the ranking vectors. In this work, building on the recently proposed NCDawareRank framework, we exploit the decomposition of the underlying space into blocks, and we derive easy to check necessary and sufficient conditions for random surfing without teleportation.Comment: 13 pages. Published in the Volume: "Algorithms, Probability, Networks and Games, Springer-Verlag, 2015". (The updated version corrects small typos/errors

Multi-layer model for the web graph

This paper studies stochastic graph models of the WebGraph. We present a new model that describes the WebGraph as an ensemble of different regions generated by independent stochastic processes (in the spirit of a recent paper by Dill et al. [VLDB 2001]). Models such as the Copying Model [17] and Evolving Networks Model [3] are simulated and compared on several relevant measures such as degree and clique distribution

Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade

We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in economic space determines particular symmetries of the network, while the observed evolution of reciprocity is consistent with a symmetry breaking taking place in production space. Our results show that networks can be strongly affected by symmetry-breaking phenomena occurring in embedding spaces, and that stochastic network symmetries can successfully suggest, or rule out, possible underlying mechanisms.Comment: Final accepted versio

Determining factors behind the PageRank log-log plot

We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiple coefficient, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Our theoretical predictions show a good agreement with experimental data on three different samples of the Web

In-Degree and PageRank of web pages: why do they follow similar power laws?

PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of PageRank, and is analogous to the well-known distributional identity for the busy period in the $M/G/1$ queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail distributions of PageRank and In-Degree differ only by a multiple factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data

A stochastic model for the evolution of the Web

Recently several authors have proposed stochastic models of the growth of the Web graph that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the "rich get richer" phenomenon. However, these models fail to explain several distributions arising from empirical results, due to the fact that the predicted exponent is not consistent with the data. To address this problem, we extend the evolutionary model of the Web graph by including a non-preferential component, and we view the stochastic process in terms of an urn transfer model. By making this extension, we can now explain a wider variety of empirically discovered power-law distributions provided the exponent is greater than two. These include: the distribution of incoming links, the distribution of outgoing links, the distribution of pages in a Web site and the distribution of visitors to a Web site. A by-product of our results is a formal proof of the convergence of the standard stochastic model (first proposed by Simon)