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 -