On October 7, 2016 Pim van der Hoorn will defend his PhD thesis. The thesis is entitled 'Asymptotic analysis of network structures: degree-degree correlations and directed paths'.The promotor is prof. dr. R.J. Boucherie and assistent promotor Dr. N. Litvak.
Location: University of Twente, Building Waaier.
Summary
The world around us is filled with complex systems. Many of these systems can be described as a network, a collection of nodes and connections between nodes. Due to the fact that these networks are often large and have a non-trivial structure, we call these complex networks.
This thesis analyzes the asymptotic properties of structural quantities in complex networks, using the framework of random graphs and regularly-varying distributions. All theoretical results are accompanied by large scale numerical experiments, using state-of-the-art algorithms, to show how well they hold up in practice.
First the correlation between the degrees of connected nodes, called degree-degree correlations, is analyzed. New measures for degree-degree correlations in directed networks are introduced as well as a model for generating networks which have a specific degree-degree correlation structure.
In addition the directed configuration model is analyzed. The asymptotic behavior of measures for degree-degree correlations in the model is determined and an expression for the distribution of the length of the shortest directed path between to random nodes is derived.
