The phase transition and connectedness in uniformly grown random graphs


We consider several families of random graphs that grow in time by the addition of vertices and edges in some 'uniform' manner. These families are natural starting points for modelling real-world networks that grow in time. Recently, it has been shown (heuristically and rigorously) that such models undergo an 'infinite-order phase transition': as the density parameter increases above a certain critical value, a 'giant component' emerges, but the speed of this emergence is extremely slow. In this paper we shall present some of these results and investigate the connection between the existence of a giant component and the connectedness of the final infinite graph. © Springer-Verlag 2004.

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)