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

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Cited by in corpus (15)

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• The entropy of network ensembles
• Explicit determination of mean first-passage time for random walks on deterministic uniform recursive trees
• Growing Multiplex Networks with Arbitrary Number of Layers
• 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
• Large deviations for the degree structure in preferential attachment schemes
• Emergence of Clusters in Growing Networks with Aging
• Random Ancestor Trees
• Degree and component size distributions in generalized uniform recursive tree
• Temporal Dynamics of Connectivity and Epidemic Properties of Growing Networks
• Rank-dependent deactivation in network evolution
• Competition and evolution in restricted space