  Let $\fg$ be the Lie superalgebra $\fgl(m,n).$ Algorithms for computing the
composition factors and multiplicities of Kac modules for $\fg$ were given by
the second author in 1996, and by J. Brundan in 2003.
  We give a combinatorial proof of the equivalence between the two algorithms.
The proof uses weight and cap diagrams introduced by Brundan and C. Stroppel,
and cancelations between paths in a graph $\mathcal{G}$ defined using these
diagrams. Each vertex of $\mathcal{G}$ corresponds to a highest weight of a
finite dimensional simple module, and each edge is weighted by a nonnegative
integer. If $\mathcal{E}$ is the subgraph of $\mathcal{G}$ obtained by deleting
all edges of positive weight, then $\mathcal{E}$ is the graph that describes
non-split extensions between simple highest weight modules.
  We also give a procedure for finding the composition factors of any Kac
module, without cancelation. This procedure leads to a second proof of the main
result.
