  We study a simple model of conducting polymers in which a single electron
propagates through a randomly tangled chain. The model has the geometry of a
small-world network, with a small density $p$ of crossings of the chain acting
as shortcuts for the electron. We use numerical diagonalisation and simple
analytical arguments to discuss the density of states, inverse participation
ratios and wave functions. We suggest that there is a critical point at $p=0$
and demonstrate finite-size scaling of the energy and wave functions at the
lower band edge. The wave functions are multifractal. The critical exponent of
the correlation length is consistent with criticality due to the small-world
effect, as distinct from the previously discussed, dimensionality-driven
Anderson transition.
