## Internet Mathematics

- Internet Math.
- Volume 1, Number 2 (2003), 193-213.

### Infinite Limits of Copying Models of the Web Graph

Anthony Bonato and Jeanette Janssen

#### Abstract

Several stochastic models were proposed recently to model the dynamic evolution of the web graph. We study the infinite limits of the stochastic processes proposed to model the web graph when time goes to infinity. We prove that deterministic variations of the so-called copying model can lead to several nonisomorphic limits. Some models converge to the infinite random graph *R*, while the convergence of other models is sensitive to initial conditions or minor changes in the rules of the model. We explain how limits of the copying model of the web graph share several properties with *R* that seem to reflect known properties of the web graph.

#### Article information

**Source**

Internet Math., Volume 1, Number 2 (2003), 193-213.

**Dates**

First available in Project Euclid: 7 July 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.im/1089229508

**Mathematical Reviews number (MathSciNet)**

MR2077225

**Zentralblatt MATH identifier**

1080.05084

**Subjects**

Primary: 05C80: Random graphs [See also 60B20] 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35] 94C15: Applications of graph theory [See also 05Cxx, 68R10]

**Keywords**

web graph evolving copying model preferential attachment model the infinite random graph adjacency property inexhaustible graph bipartite cores Hamilton paths

#### Citation

Bonato, Anthony; Janssen, Jeanette. Infinite Limits of Copying Models of the Web Graph. Internet Math. 1 (2003), no. 2, 193--213. https://projecteuclid.org/euclid.im/1089229508