D. S. Callaway J. E. Hopcroft J. M. Kleinberg M. E. J. Newman S. H. Strogatz
Abstract
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability \delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time steps. In the limit of large t, the resulting graph displays surprisingly rich characteristics. In particular, a giant component emerges in an infinite-order phase transition at \delta = 1/8. At the transition, the average component size jumps discontinuously but remains finite. In contrast, a static random graph with the same degree distribution exhibits a second-order phase transition at \delta = 1/4, and the average component size diverges there. These dramatic differences between grown and static random graphs stem from a positive correlation between the degrees of connected vertices in the grown graph--older vertices tend to have higher degree, and to link with other high-degree vertices, merely by virtue of their age. We conclude that grown graphs, however randomly they are constructed, are fundamentally different from their static random graph counterparts.
Download Info
To our knowledge, this item is not available for
download. To find whether it is available, there are three
options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page
whether it is in fact available.
3. Perform a search for a similarly titled item that would be
available.
Publisher Info
Paper provided by Santa Fe Institute in its series Working Papers with number
01-05-025.