Identification of a current-carrying subset of a percolation cluster using a modified wall follower algorithm

TL;DR

This paper introduces a modified wall follower algorithm to efficiently identify the current-carrying backbone of percolation clusters, demonstrated on networks of conductive sticks, revealing rapid percolation threshold behavior.

Contribution

A novel modification of the wall follower algorithm enables backbone identification without exhaustive edge traversal in percolation networks.

Findings

Percolation cluster strength approaches unity above threshold

Backbone comprises the cluster plus simple dead ends

Algorithm efficiently identifies the backbone in conductive networks

Abstract

We have proposed and implemented a modification of the well-known wall follower algorithm to identify a backbone (a current-carrying part) of the percolation cluster. The advantage of the modified algorithm is identification of the whole backbone without visiting all edges. The algorithm has been applied to backbone identification in networks produced by random deposition of conductive sticks onto an insulating substrate. We have found that (i) for concentrations of sticks above the percolation threshold, the strength of the percolating cluster quickly approaches unity; (ii) simultaneously, the percolation cluster is identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of unit degree.