  We consider a honeycomb network built of quantum wires, with each node of the
network having a Y-junction of three wires with a ring through which flux can
be inserted. The junctions are the basic circuit elements for the network, and
they are characterized by 3 x 3 conductance tensors. The low energy stable
fixed point tensor conductances result from quantum effects, and are determined
by the strength of the interactions in each wire and the magnetic flux through
the ring. We consider the limit where there is decoherence in the wires between
any two nodes, and study the array as a network of classical 3-lead circuit
elements whose characteristic conductance tensors are determined by the quantum
fixed point. We show that this network has some remarkable transport properties
in a range of interaction parameters: it has a Hall resistance quantized at
Rxy=h/e^2, although the longitudinal resistivity is non-vanishing. We show that
these results are robust against disorder, in this case non-homogeneous
interaction parameters g for the different wires in the network.
