Visiting Speaker
Johan van Leeuwaarden
Professor of Mathematics at Eindhoven University of Technology
Clustering spectrum of hierarchical scale-free networks
Jun 28, 2017
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3:00 pm
177 Huntington Ave
11th floor
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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.

about the speaker
Johan van Leeuwaarden (1978) is professor of mathematics at Eindhoven University of Technology. He chairs the group Stochastic Networks and Applied Probability and investigates phenomena arising in complex networks, such as communication networks, social networks and biological networks, primarily through stochastic models (random graphs, interacting particles and queueing networks), in particular their scaling limits and asymptotic behavior. Johan is member of the Young Academy (part of The Royal Netherlands Academy of Arts and Sciences) and promotes the role of mathematics and data in the networked society. He also co-founded the large multidisciplinary research program NETWORKS (

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