This announcement offers two full-time PhD positions (4-year contracts) funded within the LOGSMS project (“Learning on Graphs: Symmetry Meets Structure”) at the Discrete Mathematics and Mathematical Programming (DMMP) group of the University of Twente’s Department of Applied Mathematics. The research addresses the mathematical foundations of machine learning on graph-structured data and networks, a rapidly growing area essential for tasks such as social network analysis, biological networks, and graph-based AI models. PhD Position 1 focuses on developing new graph-theoretic frameworks to analyse learning models on graphs, including Graph Neural Networks (GNNs) and Graph Transformers. PhD Position 2 centres on designing scalable graph learning models to assist combinatorial solvers for practical algorithm benchmarks, grounding theoretical advances in computational practice. Fields: Machine Learning on Graphs, Graph Theory, Discrete Mathematics, Learning Theory, Algorithm Design, Network Data Science. Employment & Benefits: The positions include a gross monthly salary ranging from approx. €3,059 (1st year) to €3,881 (4th year) under the Dutch university salary scale (CAO-NU), plus holiday allowance, end-of-year bonus, pension scheme, generous leave hours, partial remote work flexibility, and access to campus facilities and Twente Graduate School training.