  The scattering amplitude in simple quantum graphs is a well-known process
which may be highly complex. In this work, motivated by the Shannon entropy, we
propose a methodology that associates to a graph a scattering entropy, which we
call the average scattering entropy. It is defined by taking into account the
period of the scattering amplitude which we calculate using the Green's
function procedure. We first describe the methodology on general grounds, and
then exemplify our findings considering several distinct groups of graphs. We
go on and investigate other possibilities, one that contains groups of graphs
with the same number of vertices, with the same degree, and the same number of
edges, with the same length, but with distinct topologies and with different
entropies. And the other, which contains graphs of the fishbone type, where the
scattering entropy depends on the boundary conditions on the vertices of degree
$1$, with the corresponding values decreasing and saturating very rapidly, as
we increase the number of elementary structures in the graphs.
