Evolving small-world networks with geographical attachment preference

Abstract

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.

11 pages, 4 figures

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• A general geometric growth model for pseudofractal scale-free web
• Farey Graphs as Models for Complex Networks
• Evolving small-world scale-free networks consist of cliques
• Geographical networks evolving with optimal policy
• Local-world evolving networks with tunable clustering
• Correlations in random Apollonian network
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Recursive weighted treelike networks
• A geometric growth model interpolating between regular and small-world networks
• From regular to growing small-world networks
• Stochastic and mixed flower graphs
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Vertex labeling and routing in expanded Apollonian networks
• Deterministic scale-free networks created in a recursive manner