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Our study is based on the work of Stinchcombe [1974 \emph{J. Phys. C}\textbf{7} 179] and is devoted to the calculations of average conductivity ofrandom resistor networks placed on an anisotropic Bethe lattice. The structureof the Bethe lattice is assumed to represent the normal directions of theregular lattice. We calculate the anisotropic conductivity as an expansion inpowers of inverse coordination number of the Bethe lattice. The expansion termsretained deliver an accurate approximation of the conductivity at resistorconcentrations above the percolation threshold. We make a comparison of ouranalytical results with those of Bernasconi [1974 \emph{Phys. Rev. B}\textbf{9} 4575] for the regular lattice.

Anisotropic generalization of Stinchcombe's solution for conductivity of random resistor network on a Bethe lattice