Effective dimensions and percolation in hierarchically structured scale-free networks

Abstract

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.

5 pages, 5 figures

References in corpus (15)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Evolution of networks
• Scaling and percolation in the small-world network model
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Pseudofractal Scale-free Web
• Highly clustered scale-free networks
• Epidemic threshold in structured scale-free networks
• Growing Scale-Free Networks with Small World Behavior
• A Geometric Fractal Growth Model for Scale Free Networks
• Scale-free Networks on Lattices
• Geography in a Scale-Free Network Model
• Topology and correlations in structured scale-free networks
• Shortest paths on systems with power-law distributed long-range connections

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