Analysis of metabolic network representations through graph neural networks

The computational modeling of metabolism requires specific representation techniques to capture the inherent complexity of biochemical networks. This thesis investigates the application of Graph Learning (GL) methodologies to classify and analyze metabolic networks derived from the KEGG database. The research focuses on three distinct levels of topological abstraction: Reaction Graphs (RGs), which model individual biochemical reactions as nodes; Metabolic Directed Acyclic Graphs (mDAGs), obtained by condensing strongly connected components (SCCs) into Metabolic Building Blocks (MBBs) to eliminate cycles; and Abstract Metabolic Networks (AMNs), which provide a high-level modular view of pathways. Methodologically, we adapt and compare two graph learning paradigms from the recent literature: the Graph Kernel Neural Network (GKNN), combining stochastic masks with graph kernels, and the Kolmogorov-Arnold Graph Neural Network (KA-GNN), which uses learnable univariate functions on the edges. Within the kernel pipeline, we introduce two original contributions: a cycle-aware Weisfeiler-Lehman variant (En-WL), designed to neutralize the redundancy of reversible reactions, and a family of node relabeling strategies (Just Reactions, JR; Separate Enzymes, SE; Enzymes and Reactions, ER). Empirical results demonstrate that both frameworks achieve high classification accuracy, with the KA-GNN outperforming the discrete model on highly heterogeneous clades like Protists. When stress-tested against severe class imbalances and topological noise across the complete KEGG dataset, the KA-GNN shows exceptional generalization robustness. Finally, a structural decoding of the learned masks reveals that the models autonomously reconstruct cohesive biological pathways rather than exploiting spurious correlations.