Transition from small to large world in growing networks

TL;DR

This paper investigates how the global structure of growing networks changes based on the attachment probability's decay rate with node age, revealing phase transitions between different dimensionalities.

Contribution

It introduces a model where attachment probability depends on node age, identifying phase transitions in network dimensionality based on decay rates.

Findings

Network is infinite- or finite-dimensional depending on decay rate.

Network becomes one-dimensional when decay is faster than (age)^{-2}.

Structural characteristics vary across phases.

Abstract

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.