The index of a fixed point class is a classical invariant in Nielsen fixed point theory. In this talk, we introduce a new invariant called the improved characteristic, and show that the two homotopy invariants mentioned above are exactly the same for every injective selfmaps of graphs. Since the improved characteristic is totally determined by the endomorphism of the fundamental group, we give a group-theoretical approach to compute indices of fixed point classes of graph selfmaps. This is joint work with ZHAO Xuezhi.