Figure 1

Graphical representation of the basic binary operations of the network algebra. Diagrams (A) and (B) summarize the citric-acid cycle of P. horikoshii and H. pylori [31]. Hypergraphs can always be drawn as bipartite graphs with one class of vertices representing the hypergraph vertices (chemical species, ●), while the other class of vertices encodes the hyperedges (chemical reactions, ■). Each reaction is connected by (directed) arrows from its educts and to its products. For clarity of presentation we have omitted the direction of the arrows (most reactions are reversible) as well as small molecules such as CO₂ and H₂O here. Furthermore, two reactions are marked in color, namely the ones catalyzed by citrate synthase in red, and pyruvate dehydrogenase in green. The results of the basic operations are as follows: (a) Intersection A ∩ B; (b) Union A ∪ B; (c) Symmetric Difference A △ B; (d) Strict Symmetric Difference A ◊ B; (e) Difference A \ B; (f) Difference B \ A.