Evolving networks with distance preferences

Abstract

We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected (``make friends with the friends of your present friends''). We present simulation results for network parameters like the first eigenvalue of the graph Laplacian (synchronizability), clustering coefficients, average distances, and degree distributions for different distance preferences and compare with the parameter values for random and scale free networks. We find that for the shortest distance rule we obtain a power law degree distribution as in scale free networks, while the other parameters are significantly different, especially the clustering coefficient.

REVTEX Format, 6 Pages, 6 Figures, 1 Table; References added and Revised

References in corpus (11)

• Statistical mechanics of complex networks
• Evolution of networks
• Clustering and preferential attachment in growing networks
• Growing Scale-Free Networks with Tunable Clustering
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• Highly clustered scale-free networks
• Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web
• Emergence of a small world from local interactions: Modeling acquaintance networks
• Spectral Properties and Synchronization in Coupled Map Lattices
• Spectra and eigenvectors of scale-free networks
• Stability of Synchronized Chaos in Coupled Dynamical Systems

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• A Tractable Complex Network Model based on the Stochastic Mean-field Model of Distance
• Extremal Properties of Random Structures
• Equilibrium statistical mechanics of network structures
• Information Dynamics in the Networked World
• Spectral plots and the representation and interpretation of biological data
• Clustering properties of a generalised critical Euclidean network
• Growing networks under geographical constraints
• Evolution of network structure by temporal learning
• Quasistatic Scale-free Networks
• Small World Graphs by the iterated "My Friends are Your Friends'' Principle
• Complex systems: features, similarity and connectivity
• Biological network comparison via Ipsen-Mikhailov distance
• An introduction to spectral distances in networks (extended version)
• Generating Scale-free Networks with Adjustable Clustering Coefficient Via Random Walks
• Local excitation-lateral inhibition interaction yields wave instabilities in spatial systems involving finite propagation delay