Figure 1
From: Properties of metabolic graphs: biological organization or representation artifacts?
Illustration of the hypergraph transformations and abstractions. Left: a hyperedge is turned into a complete graph linking every pair of nodes to obtain the primal graph (I). Middle: the cis- (II) and trans-primal (III) graphs are obtained by connecting either nodes in the same side of the hyperedge partition or on different sides, respectively. Right: The physical line graph transformation (IV) can be obtained by taking the primal of the dual of the hypergraph; that is, it is the composition of two transformations.