Does a network of monotone resistors have an operating point?

This work is a sequel to a prior work that established a procedure for determining whether or not a series parallel network of continuous strictly monotonically increasing resistors with restricted domains and ranges has an operating point. Herein we accomplish the same thing, but this time for networks with arbitrary graphs. That is, the series-parallel restriction is now removed. This substantially expands the applicability of our result. Moreover, our procedure is highly efficient for the following reasons: We characterize each resistor by only four numbers (-∞ and +∞ allowed) determined by the asymptotes to which the resistor´s characteristic curve approaches. It is only these numbers that are added or subtracted to test for the existence of an operating point. Furthermore, the numerical complexity of our procedure increases only linearly with the number of branches in the network. All this is accomplished without a computation of the operating point, which can be an onerous task that will perforce end in failure if the operating point does not exist