  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 $O\left(\sqrt{N_\text{V}}\right)$ to $\Theta(N_\text{V})$. 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.
