A novel and simple method of fabrication of mesoscopic honeycomb-shaped networks was applied in order to decrease the dimension of the 2-D gas with electron density of approximately 1×1012 cm−2 in the initial GaAs/AlGaAs δ-doped heterostructures. The characteristic dimensions of the size of hexagonal cell and the thickness of bonds of the network were approximately 500 and 70 nm, respectively. Magnetoresistance in pulsed magnetic fields up to 34 T, current-voltage (I(V )) curves and the temperature dependence of resistance in the mesoscopic networks were measured at temperatures 1.9–300 K. At B=0, the behaviour of the resistance is typical of a two-dimensional insulator. Below approximately 20 K, the data follows the Mott variable-range-hopping mechanism for 2-D. The observed negative magnetoresistance at low magnetic fields was related to quantum interference in the variable range hopping. At magnetic fields higher than approximately 5 T, the magnetoresistance is positive and saturates at fields B>12 T.