  From any given sequence of finite or infinite graphs, a nonstandard graph is
constructed. The procedure is similar to an ultrapower construction of an
internal set from a sequence of subsets of the real line, but now the
individual entities are the vertices of the graphs instead of real numbers. The
transfer principle is then invoked to extend several graph-theoretic results to
the nonstandard case. After incidences and adjacencies between nonstandard
vertices are defined, several formulas regarding numbers of vertices and edges,
and nonstandard versions of Eulerian graphs, Hamiltonian graphs, and a coloring
theorem are established for these nonstandard graphs.
