I am a PhD Candidate in Mathematics. My research interests mainly concern Probability and Stochastics: in particular, my project studies the structure and motifs of inhomogeneous geometric random graphs and networks.

I received my MSc from the University of Padua, Italy, in 2020. My math background is on probability theory, and my education is mainly based on the development of abstract thought, in accordance with the Italian tradition.

## Expertise

#### Mathematics

- Vertex
- Random Graph
- Geometry
- Clique
- Hyperbolic Geometry

#### Computer Science

- Models
- Random Graphs
- Real World

## Organisations

You can find my publications and works here:

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Here is a list of my current research interests:

**Random graphs**

Random graphs are probability distributions over graphs. Equivalently, they are graphs built through a random process. They are used for different purposes, such as: proving existence of (deterministic) graphs with specific properties; modeling complex networks encountered in different areas, from biology to social sciences; characterizing the typical elements of graph ensambles. My research interest concerns inhomogeneous and geometric random graphs

**Geometric networks**

Networks may often be embedded in metric spaces, where each vertex is assigned a position. In real contexts, it is natural to expect that two nearby vertices connect more easily than two distant vertices. When this happens, we say that the network is geometric. I am interested in studying this kind of networks mathematically, analyzing the properties of geometric models and understanding what differs in presence or absence of geometry.

**Network structure**

Many real world networks have been found to be scale-free: they have a power-law degree distribution, meaning they are self-similar, with a global fractal structure. On the other hand, large network often possess non-trivial topological properties, which considerably complicate the local analysis of the system. Part of my work, is to reconstruct the local structure of different network models. Studying network motifs and clustering is one way to achieve such result.

## Publications

*Journal of applied probability*(E-pub ahead of print/First online). Deijfen, M. & Michielan, R.https://doi.org/10.1017/jpr.2024.18Optimal subgraphs in geometric scale-free random graphs. ArXiv.org. Michielan, R., Stegehuis, C. & Walter, M.https://doi.org/10.48550/arXiv.2404.14972

*Physical Review E, 106*(5), Article 054303. Michielan, R., Litvak, N. & Stegehuis, C.https://doi.org/10.1103/PhysRevE.106.054303Detecting hyperbolic geometry in networks: why triangles are not enough. ArXiv.org. Litvak, N., Michielan, R. & Stegehuis, C.https://doi.org/10.48550/arXiv.2206.01553Cliques in geometric inhomogeneous random graphs

*Journal of Complex Networks, 10*(1), Article cnac002. Michielan, R. & Stegehuis, C.https://doi.org/10.1093/comnet/cnac002

## Research profiles

## Courses academic year 2023/2024

Courses in the current academic year are added at the moment they are finalised in the Osiris system. Therefore it is possible that the list is not yet complete for the whole academic year.

## Courses academic year 2022/2023

## Address

### University of Twente

Zilverling (building no. 11)

Hallenweg 19

7522 NH Enschede

Netherlands

### University of Twente

Zilverling

P.O. Box 217

7500 AE Enschede

Netherlands

## Organisations

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