Vilhelm Agdur

🧩

Vilhelm Agdur

PhD Student

Uppsala University

About Me

Vilhelm Agdur is a PhD student at Uppsala University, working on community detection problems in graphs, from a combinatorial and algorithmic perspective. As a teacher, he has lectured courses on graph theory and combinatorics, and supervised two bachelor’s theses.

Interests

Graph Theory
Machine Learning

Education

PhD Mathematics
Uppsala University
BSc & MSc Mathematics
Gothenburg University

📚 My Work

I am a mathematician by training, with a primary focus on community detection methods in graphs, from a combinatorial and algorithmic perspective. On September 26th, I will be defending a PhD thesis on this topic! 🤞

During my PhD, I’ve done quite a bit of teaching, being the responsible lecturer for two different courses, developing the materials and structure for one of them. I also supervised two bachelor’s theses.

In my spare time from working on my research – (as surprising as it is that I would have any) – I have coded up a few hobby projects, mostly about processing or visualising data. Check out the projects section for a selection of that! 😃

Publications

Temporal Modularity

Temporal Graphs

Temporal Modularity

This project is still ongoing, but should result in a paper within a month or two. We investigate community detection in temporal graphs, that is, graphs which evolve over time, and study the computational complexity of this problem.

Jun 1, 2025

A classification of overlapping clustering schemes for hypergraphs

Category Theory

A classification of overlapping clustering schemes for hypergraphs

In reality, friend groups often overlap, and some publications do belong both to biology and chemistry. Yet the most commonly used and studied community detection methods assume that all communities are distinct, with binary assignments to communities.

May 15, 2025

Fixed-parameter tractability of the mixed-sign k-part minimum edge cut problem on sparse graphs

Fixed-parameter tractability of the mixed-sign k-part minimum edge cut problem on sparse graphs

When applying community detection methods such as modularity, one encounters an optimization problem of the general form “I have a collection of objects that I need to divide into bags, and for each pair there is a cost or benefit associated to putting them in the same bag”. In general, this problem is very hard to solve, but for some particular instances, it is known to be easy when dividing into two bags.

May 1, 2025

Universal lower bound for community structure of sparse graphs

Community Detection

Universal lower bound for community structure of sparse graphs

When applying community detection in practice, one of the most commonly used methods is to try to find a partition that achieves a high modularity. Unfortunately, this is not a statistically justified method, and so it is in general unclear how to determine if the partition one finds is actually significant, or just the product of random noise.

Jul 14, 2023