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- Béla Bollobás, Svante Janson, Oliver Riordan
- Random Struct. Algorithms
- 2007

The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the… (More)

- Béla Bollobás, Oliver Riordan, Joel H. Spencer, Gábor E. Tusnády
- Random Struct. Algorithms
- 2001

Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at… (More)

- Béla Bollobás, Oliver Riordan
- Combinatorica
- 2004

We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probability… (More)

We introduce a model for directed scale-free graphs that grow with preferential attachment depending in a natural way on the in- and out-degrees. We show that the resulting in- and out-degree… (More)

We study percolation in the following random environment: let Z be a Poisson process of constant intensity on R 2 , and form the Voronoi tes-sellation of R 2 with respect to Z. Colour each Voronoi… (More)

- Noga Alon, Jaroslaw Grytczuk, Mariusz Haluszczak, Oliver Riordan
- Random Struct. Algorithms
- 2002

A vertex coloring of a graph G is k-nonrepetitive if one cannot find a periodic sequence with k blocks on any simple path of G. The minimum number of colors needed for such coloring is denoted by… (More)

- Béla Bollobás, Oliver Riordan
- Internet Mathematics
- 2003

- Oliver Riordan
- 2009

Recently, Bollobás, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with Θ(n) edges. Roughly speaking, there is one model for each… (More)

- Béla Bollobás, Svante Janson, Oliver Riordan
- Random Struct. Algorithms
- 2011

In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from… (More)

- Oliver Riordan, Nicholas C. Wormald
- Combinatorics, Probability & Computing
- 2010

In this paper we study the diameter of the random graph G(n, p), i.e., the the largest finite distance between two vertices, for a wide range of functions p = p(n). For p = λ/n with λ > 1 constant,… (More)