https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2MBS80&collegejaar=2025&taal=enComplex networks are all around us. Think of social networks of friends and acquaintances you have formed, biological networks where cells exchange proteins with each other in your body, or transportations networks that keep us all physically connected. In this course, you will gain insight into the basic properties of real-life networks and the fundamental mathematical techniques in order to understand how real-life network properties can mathematically emerge. The course consists of an introductory module and three content modules. In the introductory module, you will familiarize yourself with mathematical terminology and basic results, as well as with Jupiter notebooks and working with real-life data. The three content modules focus, respectively, on three fundamental properties of real-life networks: 1) sparsity; 2) presence of triangles, cliques, and other patterns; 3) network communities. Each module ends with a project on real-life data in Jupiter notebooks (no report), and a short written test with multiple attempts. The grade will be defined by your results in the projects and the tests of the three content modules. The final exam will be used to retry some of the module tests if needed. This is a hands-on course. The students must be present in-person.
Learning objectives:
- You can define and extract properties of real-life networks.
- You can reflect on the implications of network properties in real-life settings.
- You can model sparse networks with the Erdös-Rényi random graph model, and verify sparsity of other random graph models.
- You can use the sum of indicators to compute the mean and the variance of the number of patterns such as triangles, wedges and cliques in a random graph.
- You can use the first and the second moment methods to derive asymptotic properties of the number of small induced subgraphs such as wedges and cliques in a sparse random graph.
- You can mathematically describe community structure in a network using the Stochastic Block Models.
- You can explain and apply spectral clustering and modularity maximization methods for community detection.
- You can relate the properties of random graph models to the properties in real-life networks.
- You can reflect on the limitations of random graph models for representing the properties of real-life networks.
Notebook exam