  We propose a measure to quantify the efficiency of classical and quantum
mechanical transport processes on graphs. The measure only depends on the
density of states (DOS), which contains all the necessary information about the
graph. For some given (continuous) DOS, the measure shows a power law behavior,
where the exponent for the quantum transport is twice the exponent of its
classical counterpart. For small-world networks, however, the measure shows
rather a stretched exponential law but still the quantum transport outperforms
the classical one. Some finite tree-graphs have a few highly degenerate
eigenvalues, such that, on the other hand, on them the classical transport may
be more efficient than the quantum one.
