Transition from small to large world in growing networks

Details Transition from small to large world in growing networks Transition from small to large world in growing networks

2007-09-19

arxiv.org/abs/0709.3094v3

EPL 81, 30004 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

10.1209/0295-5075/81/30004

We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether the attachment probability decays slower or faster than $(age)^{-1}$. The network becomes one-dimensional when the attachment probability decays faster than $(age)^{-2}$. We describe structural characteristics of these phases and transitions between them.

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