  We consider a sequence of finite quantum graphs with few loops, so that they
converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree.
We assume these quantum trees are spectrally delocalized in some interval $I$,
in the sense that their spectrum in $I$ is purely absolutely continuous and
their Green's functions are well controlled near the real axis. We furthermore
suppose that the underlying sequence of discrete graphs is expanding. We deduce
a quantum ergodicity result, showing that the eigenfunctions with eigenvalues
lying in $I$ are spatially delocalized.
