  Kirchhoff-type Laws for signed graphs are characterized by generalizing
transpedances through the incidence-oriented structure of bidirected graphs.
The classical $2$-arborescence interpretation of Tutte is shown to be
equivalent to single-element Boolean classes of reduced incidence-based cycle
covers, called contributors. A generalized contributor-transpedance is
introduced using entire Boolean classes that naturally cancel in a graph;
classical conservation is proven to be property of the trivial Boolean classes.
The contributor-transpedances on signed graphs are shown to produce
non-conservative Kirchhoff-type Laws, where every contributor possesses the
unique source-sink path property. Finally, the maximum value of a
contributor-transpedance is calculated through the signless Laplacian.
