###### Johan van Leeuwaarden

Real-world networks often have power-law degrees and scale-free properties such as ultra-small distances and ultra-fast information spreading. We provide evidence of 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 c(k) scales with k and discover a universal curve that consists of three k-ranges where c(k) remains flat, starts declining, and eventually settles on a power law with an exponent that depends 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.

## Want to be notified about upcoming NetSI events? Sign up for our email list below!

Thank you! You have been added to our email list.

Oops! Something went wrong while submitting the form

###### Johan van Leeuwaarden

****

Real-world networks often have power-law degrees and scale-free properties such as ultra-small distances and ultra-fast information spreading. We provide evidence of 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 c(k) scales with k and discover a universal curve that consists of three k-ranges where c(k) remains flat, starts declining, and eventually settles on a power law with an exponent that depends 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.