TY - JOUR

T1 - Clustering spectrum of scale-free networks

AU - Stegehuis, C.

AU - van der Hofstad, R.W.

AU - Janssen, A.J.E.M.

AU - van Leeuwaarden, J.S.H.

PY - 2017/10/26

Y1 - 2017/10/26

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85032566863&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.042309

DO - 10.1103/PhysRevE.96.042309

M3 - Article

C2 - 29347510

VL - 96

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 042309

ER -