We mimic random nanowire networks by the homogeneous, isotropic, and random deposition of conductive
zero-width sticks onto an insulating substrate. The number density (the number of objects per unit area of the
surface) of these sticks is supposed to exceed the percolation threshold, i.e., the system under consideration is a
conductor. To identify any current-carrying part (the backbone) of the percolation cluster, we have proposed and
implemented a modification of the well-known wall follower algorithm—one type of maze solving algorithm.
The advantage of the modified algorithm is its identification of the whole backbone without visiting all the edges.
The complexity of the algorithm depends significantly on the structure of the graph and varies from O(√NV) to
O(NV). The algorithm has been applied to backbone identification in networks with different number densities
of conducting sticks. We have found that (i) for number densities of sticks above the percolation threshold, the
strength of the percolation cluster quickly approaches unity as the number density of the sticks increases; (ii)
simultaneously, the percolation cluster becomes identical to its backbone plus simplest dead ends, i.e., edges that
are incident to vertices of degree 1. This behavior is consistent with the presented analytical evaluations.