The structure of the GE detailed in the next section is such that the origin s is connected to every node of a semicomplete directed sub-network that is a generalization of its corresponding tournament (a directed graph where every pair of nodes is jointed by a single link with a unique direction) that always has a directed Hamiltonian path according to Rédei's theorem (see, eg, Bang-Jensen and Gutin, 2001, p. 14