Phd Student

## W.L.F. van der Hoorn (Pim), MSc

University of Twente

Stochastic Operations Research Group

Download thesis: Asymptotic analysis of network structures: degree-degree correlations and directed paths

**Symposium: Advances in Random Graphs and Complex Networks on October 7 ^{th}!**I am organizing a symposium on the topic of random graphs and complex networks in the morning and afternoon before the public defense of my thesis, on Friday October 7

^{th}. For more details and registration (

**no fee!**) click here.

## Current research

My research focuses on the analysis of degree-degree dependencies in networks and their influence on structural properties of those networks. I combine the theory of random graphs with large scale computer simulations to develop mathematical tools for analysis of degree-degree dependencies in directed networks which have scale-free degree distributions and apply these tools to large real-world network datasets, for instance the full English Wikipedia graph.

Tools for proper analysis of degree-degree dependencies consist of statistically consistent measures, a null model for those measures and understanding the behavior of those measures on this null model. The latter usually includes central limit theorems for those measures on the model.

I have already introduced measures for degree-degree dependencies, based on rank correlations, and showed that these are consistent estimators on a large class of random graph models. Following these results, I showed that the configuration model can be used as a null model for degree-degree correlations. In addition I investigated the influence of the removal of edges, as done in the erased configuration model, on the degree-degree correlations. Here I found a non-trivial scaling in the speed of convergence for the measures I introduced in this model, based on the exponents of the degree distributions, and established the different speeds.

Currently I am working on several projects. One is on proving central limit theorems for both the measures I proposed in the directed configuration model and the number of erased edges in the erased configuration model. Another deals with the construction and structure of graphs that are maximally disassortative, including a general characterization of the joint degree distribution.

I am also studying distances in directed configuration model, using a novel and direct branching process argument. The main goal in the future is to prove concentration of the distances between two randomly selected nodes in networks with specific degree-degree correlations.

My research is part of the EU funded project NADINE.

## Research interests

- Directed random graph models
- Complex networks
- Statistics on Networks
- Approximation algorithms for networks
- Applications of network analysis to Neuroscience
- Convergence of sequences of random graphs
- Graphons
- Category Theory

## Publications

A list of all my publications and unpublished work can be found here.

Or you can look at my arXiv profile.

## Presentations

For a list of presentations, including pdf files look here.