GraphPlot[
Table[{#1[[i]] -> #1[[1 + i]], i}, {i, 1, Length[#1] - 1}] &[
SequenceAlignment[
"GAGCGCTTTCGCGTCTACGTGCGAGATGTTGCCCGAATAAGACGTGTACCCGATAATTCTCAGTCT\
AGCTTCGGGATGCT",
"TCTCGATGCCTTTTTGTGGCGGGTCCCACAACCCCAACCTCCTTTAAACAAACAGTGTATGTCAGC\
TCAGAGTGAGTGTA"]]]