Uniqueness of electrical currents in a network of finite total resistance

TL;DR

This paper proves that in finite total resistance electrical networks, the current distribution is unique when no flow escapes to infinity, highlighting conditions for uniqueness in such networks.

Contribution

It establishes the uniqueness of electrical currents in networks with finite total resistance under specific boundary conditions, extending understanding of network behavior.

Findings

Unique electrical current in finite resistance networks

No flow escape to infinity ensures uniqueness

Conditions for current distribution in complex networks

Abstract

We show that if the sum of the resistances of an electrical network $N$ is finite, then there is a unique electrical current in $N$ provided we do not allow, in a sense, any flow to escape to infinity.