Abstract
Random rewiring is used to generate null networks for the purpose of analyzing the topological properties of scale-free networks, yet the effects of random rewiring on the degree correlation are subject to contradicting interpretations in the literature. We comprehensively analyze the degree correlation of randomly rewired scale-free networks and show that random rewiring increases disassortativity by reducing the average degree of the nearest neighbors of high-degree nodes. The effect can be captured by the measures of the degree correlation that consider all links in the network, but not by analogous measures that consider only links between degree peers, hence the potential for contradicting interpretations. We furthermore find that random and directional rewiring affect the topology of a scale-free network differently, even if the degree correlation of the rewired networks is the same. Consequently, the network dynamics is changed, which is proven here by means of the biased random walk.
Highlights
Random rewiring is used to generate null networks for the purpose of analyzing the topological properties of scale-free networks, yet the effects of random rewiring on the degree correlation are subject to contradicting interpretations in the literature
Influential was the finding that large networks tend to self-organize in a scale-free state[25] characterized by the power-law distribution, P (k) ∼ k−γ, of the connection degree, k, of nodes—a property radically different from the Poisson distribution observed in random networks
We examined the effects of random rewiring on the degree correlation of scale-free networks and found them to be disassortative after random rewiring
Summary
Either one of the new links already exist, the rewiring step is aborted. Irrespective of whether a single step was successful or aborted, the whole procedure is repeated starting with the random selection of two different pre-existing links. Following these steps guarantees that a pair of nodes defines a unique link and that the degree of nodes remains unaffected by rewiring. Several measures of the degree correlation have been proposed in the literature. They can roughly be classified into two types; measures that consider (i) all links in the network or (ii) just links between degree peers.
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