Transition from small to large world in growing networks

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.

5 pages

References in corpus (6)

• Critical phenomena in complex networks
• A geometric growth model interpolating between regular and small-world networks
• Universal Scaling Behavior of Clustering Coefficient Induced by Deactivation Mechanism
• Transition from small to large world in growing networks
• From regular to growing small-world networks
• Scale-free networks with a large- to hypersmall-world transition

Cited by in corpus (7)

• Critical phenomena in complex networks
• The entropy of network ensembles
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks
• Transition from small to large world in growing networks
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Degree and component size distributions in generalized uniform recursive tree