  We give entropy estimates for two canonical non commutative shifts on
$C^*$-algebras associated to some topological graphs $E=(E^0,E^1,s,r)$, defined
using a basis of the corresponding Hilbert bimodule $H(E)$. We compare their
entropies with the growth entropies associated directly to the topological
graph. We illustrate with some examples of topological graphs considered by
Katsura, where the vertex and the edge spaces are a union of unit circles and
more detailed computations can be done.
