Abstract
The macroscopic conductivity sigma e of a simple cubic, two-component, random resistor network is systematically expanded as a power series in the relative difference between the two basic conductances. Graphs are developed to aid in implementing the calculation. A single-bond T-matrix-type rearrangement of the series leads to various types of single-bond approximations, and to an improved graph expansion for sigma e. The improved expansion is worked out up to seventh order, and used to discuss the singular properties of sigma e.