Clustering spectrum of scale-free networks

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Real-world networks often have power-law degrees and scale-free properties, such as ultrasmall distances and ultrafast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the creation of triangles and signal the presence of hierarchy. We quantify this property in terms of c(k), the probability that two neighbors of a degree-k node are neighbors themselves. We investigate how the clustering spectrum k↦c(k) scales with k in the hidden-variable model and show that c(k) follows a universal curve that consists of three k ranges where c(k) remains flat, starts declining, and eventually settles on a power-law c(k)∼k^α with α depending on the power law of the degree distribution. We test these results against ten contemporary real-world networks and explain analytically why the universal curve properties only reveal themselves in large networks.
Original languageEnglish
Article number042309
Number of pages15
JournalPhysical Review E
Issue number4
Publication statusPublished - 26 Oct 2017


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