The focus of this PhD fellowship lies on method development in representation learning for graphs, similarity measures and clustering methods for graphs. Relationship graphs extracted from data have the potential to describe correlations and dependencies among objects in a dataset beyond pairwise interactions, and are crucial to quantify complex relationships in, e.g., spatial omics. Generally, these relationship graphs may vary in number of nodes and edges, and additionally have labelled nodes, which makes comparison of such graphs very challenging. Furthermore, we want to incorporate knowledge of an underlying semantic relationship between the nodes of the graphs, independent of the extracted spatial graphs themselves which should be integrated using suitable representations and embeddings.