  Metabolic networks are probably among the most challenging and important
biological networks. Their study provides insight into how biological pathways
work and how robust a specific organism is against an environment or therapy.
Here we propose a directed hypergraph with edge-dependent vertex weight as a
novel framework to represent metabolic networks. This hypergraph-based
representation captures higher-order interactions among metabolites and
reactions, as well as the directionalities of reactions and stoichiometric
weights, preserving all essential information. Within this framework, we
propose the communicability and the search information as metrics to quantify
the robustness and complexity of directed hypergraphs. We explore the
implications of network directionality on these measures and illustrate a
practical example by applying them to the small-scale e\_coli\_core model.
Additionally, we compare the robustness and the complexity of 30 different
models of metabolism, connecting structural and biological properties. Our
findings show that antibiotic resistance is associated with high structural
robustness, while the complexity can distinguish between eukaryotic and
prokaryotic organisms.
