Correlations in Scale-Free Networks: Tomography and Percolation

Abstract

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabasi-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussig the shell structure of the networks around their arbitrary node. In spite of different correlation behavior, all three constructions exhibit similar percolation properties.

6 pages, 2 figures; added references

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Cited by in corpus (8)

• Extending the definition of modularity to directed graphs with overlapping communities
• Resilience of public transport networks against attacks
• Construction and properties of assortative random networks
• Percolation transition in networks with degree-degree correlation
• Degree Correlation in Scale-Free Graphs
• Growing networks under geographical constraints
• On the Tomography of Networks and Multicast Trees
• Finite size effects in Barabasi-Albert growing networks