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Open AccessJournal ArticleDOI

A stochastic model for the evolution of the Web

Mark Levene, +3 more
- 21 Jun 2002 - 
- Vol. 39, Iss: 3, pp 277-287
TLDR
In this article, the authors extend the evolutionary model of the Web graph by including a non-preferential component, and view the stochastic process in terms of an urn transfer model.
About: 
This article is published in Computer Networks.The article was published on 2002-06-21 and is currently open access. It has received 64 citations till now. The article focuses on the topics: Simon model & Stochastic modelling.

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Journal ArticleDOI

Meeting Strangers and Friends of Friends: How Random are Social Networks?

Matthew O. Jackson, +1 more
- 01 May 2007 - 
TL;DR: It is shown that as the random/network-based meeting ratio varies, the resulting degree distributions can be ordered in the sense of stochastic dominance, which allows us to infer how the formation process affects average utility in the network.
Book ChapterDOI

The Economics of Social Networks

Matthew O. Jackson
- 01 Aug 2005 - 
TL;DR: The aim is to provide some perspective on the research from these literatures, with a focus on the formal modeling of social networks and the two major types of models: Those based on random graphs and those based on game theoretic reasoning.
Book ChapterDOI

Using PageRank to Characterize Web Structure

Gopal Pandurangan, +2 more
TL;DR: This work studies the distribution of PageRank values (used in the Google search engine) on the Web, and develops detailed models for the Web graph that explain this observation, and remain faithful to previously studied degree distributions.
Book

An Introduction to Search Engines and Web Navigation

Mark Levene
TL;DR: This book demystifies the tools that the authors use when interacting with the web, and gives the reader a detailed overview of where they are and where they are going in terms of search engine and web navigation technologies.
Journal ArticleDOI

Likelihood-based inference for stochastic models of sexual network formation.

Mark S. Handcock, +1 more
- 01 Jun 2004 - 
TL;DR: No single unitary process clearly underlies the formation of these sexual networks, and substantial model uncertainty exists for sexual network degree distributions, which suggests behavioral heterogeneity plays an essential role in network structure.
References
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Book

Handbook of mathematical functions : with formulas, graphs, and mathematical tables

Milton Abramowitz, +1 more
Proceedings ArticleDOI

On power-law relationships of the Internet topology

Michalis Faloutsos, +2 more
TL;DR: These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period, and can be used to generate and select realistic topologies for simulation purposes.
Journal ArticleDOI

Graph structure in the Web

Andrei Z. Broder, +7 more
TL;DR: The study of the web as a graph yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution.
Journal ArticleDOI

On a class of skew distribution functions

Herbert A. Simon
- 01 Dec 1955 - 
TL;DR: In this paper, the authors analyse a class of distribution functions that appear in a wide range of empirical data-particularly data describing sociological, biological and economic phenomena-and look for an explanation of the observed close similarities among the five classes of distributions listed above.
Journal ArticleDOI

Mean-field theory for scale-free random networks

Albert-László Barabási, +2 more
- 01 Oct 1999 - 
TL;DR: A mean-field method is developed to predict the growth dynamics of the individual vertices of the scale-free model, and this is used to calculate analytically the connectivity distribution and the scaling exponents.
Frequently Asked Questions (8)
Q1. What are the contributions mentioned in the paper "A stochastic model for the evolution of the web" ?

By making this extension, the authors can now explain a wider variety of empirically discovered power-law distributions provided the exponent is greater than two. 

In their case, when α is not necessarily zero, by using (2) instead of the more natural (6), there is no problem in computing the expectation of Fi(k), since the parameter p is a constant, allowing us to find the expected value of Fi(k) by using the linearity of expectations. 

Fi(k)k(1 + αp) + α(1− p) , (1)a new ball is added to urn1 (provided that 0 ≤ pk+1 ≤ 1) or,(ii) with probability 1− pk+1, an urn is selected − urni being chosen with probability(1− p)(i + α) 

It can be verified that the probability that p3 be ill-defined is 0.15, that p4 be ill-defined is about 0.1905, that p5 be ill-defined is about 0.1769 and that p6 be ill-defined is 0. 

In the discussion at the end of Section 3 the authors suggest that, in practice, starting from a typical initial configuration of balls in the urns, it is likely that pk+1 will be well defined for all k, even if (5) does not hold. 

The probability (2) is a combination of a preferential component (proportional to the number of pins in urni) and a non-preferential component (proportional to the number of balls in urni). 

As far as the authors are aware, their convergence proof given in the Appendix is the first formal proof validating Simon’s model − it does not rely on the mean-field theory approach, as for example in [BAJ99]. 

A situation when α > 0 might occur if there is a choice of Web pages to link to and the actual decision of which links are put in place has a random component.