Correlations in Scale-Free Networks: Tomography and Percolation

TL;DR

This paper compares three models of scale-free networks with identical degree distributions but different correlation properties, analyzing their structure and percolation behavior.

Contribution

It introduces and compares three related scale-free network models, highlighting how correlation properties affect their structure and percolation characteristics.

Findings

Barabasi-Albert model shows dissortative degree correlations.

Node-randomized network exhibits assortative mixing.

All models have similar percolation properties despite different correlations.

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.