  We present the theory of multifunctions applied to graphs. Its interesting
feature is that walks are recognized as iterations. We consider the graphs with
arbitrary number of vertices which are determined by multifunctions. The
mutually unique correspondence between graphs and multifunctions is proven. We
explain that many facts of graph theory can be formulated in the language of
multifunctions and as examples we give$\colon$ neighborhood, walk, independent
set, clique, bipartiteness, connectedness, isolated vertices, graph metric,
leaf. To simplify the proofs of our theorems, we introduce the concept of
iterations of multifunctions. The new equivalent conditions for bipartite
multifunctions including the K\"onig theorem and even iterations theorem are
given. We prove that there exist filters and ideals in graph theory that are
similar to those from the set theory. Finally, to illustrate these facts, we
consider the multifunction of prime numbers.
