Transition from small to large world in growing networks

Understand

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.