  We study multiport networks, common in electrical engineering. They have
boundary conditions different from electrical networks: the boundary vertices
are split into pairs and the sum of the incoming currents is set to be zero in
each pair. If one sets the voltage difference for each pair, then the incoming
currents are uniquely determined. We generalize Kirchhoff's matrix-tree theorem
to this setup. Different forests now contribute with different signs, making
the proof subtle. In particular, we use the formula for the response matrix
minors by R. Kenyon-D. Wilson, determinantal identities, and combinatorial
bijections. We introduce superport networks, generalizing both ordinary
networks and multiport ones.
