Abstract
In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects k possible partners from the existing network and joins them with probability by undirected edges. The “activity” of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for There is no giant component formed for any and thus in this sense there is no phase transition. However, the average component size diverges for
- Received 13 May 2003
DOI:https://doi.org/10.1103/PhysRevE.68.066104
©2003 American Physical Society