  In this paper we will prove that there exists a covariant functor from the
category of schemes to the category of graphs. This functor provides a
combination between algebraic varieties and combinatorial graphs so that the
invariants defined on graphs can be introduced to algebraic varieties in a
natural manner. By the functor, we will define the combinatorial norm of a
morphism of schemes. Then we will obtain some properties of morphisms of norm
not great than one. The topics discussed here can be applied to study the
discrete Morse theory on arithmetic schemes and Kontsevich's theory of graph
homology.
