Endomorphisms of graph C*-algebras are investigated. A combinatorial ap-
proach to analysis of permutative endomorphisms is developed. Then invertibility
criteria for localized endomorphisms are given. Furthermore, proper endomor-
phisms which restrict to automorphisms of the canonical diagonal MASA are
analyzed. The Weyl group and the restricted Weyl group of a graph C*-algebra
are introduced and investigated. Criteria of outerness for automorphisms in the
restricted Weyl group are found
