Eur. Phys. J. B 30, 143-146 (2002)
https://doi.org/10.1140/epjb/e2002-00368-5

Voltage distribution in growing conducting networks

¹ Jožef Stefan Institute, PO Box 3000, 1001 Ljubljana, Slovenia
² Bogolubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research, 141980 Dubna, Russia

Corresponding author: ^a Bosiljka.Tadic@ijs.si

Received: 26 August 2002
Published online: 29 November 2002

Abstract

We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the current through the emergent conducting graph, representing a digital circuit. In the interior of a large network the voltage varies with the addition time s<t of the node as when constant current enters the network at last added node t and leaves at the root of the graph which is grounded. The topological closeness of the conduction path and shortest path through a node suggests that the charged random walk determines these global graph properties by using only local search algorithms. The results agree with mean-field theory on tree structures, while the numerical method is applicable to graphs of any complexity.