  The spectral properties of the Laplacian on a class of quantum graphs with
random metric structure are studied. Namely, we consider quantum graphs spanned
by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the
vertices, and we assume that the edge lengths are randomly independently
identically distributed. Under the assumption that the coupling constant at the
vertices does not vanish, we show that the operator exhibits the Anderson
localization at the bottom of the spectrum almost surely. We also study the
case of other spectral edges.
