Monotone Multiterminal Resistors and Large Networks

We show how the set of strongly monotone and Lipschitz multiterminal resistors is closed under forming networks and choosing terminals. We show that an infinite network of multiterminal resistors can serve as an approximation for all large finite subnetworks. We show that we may obtain the hierarchy of infinite networks of A. Zemanian from the set of multiterminal resistors. The techniques include new notation, nodal analysis and loop space analysis.