  We investigate the localization behavior of electrons in a random lattice
which is constructed from a quasi-one-dimensional chain with large coordinate
number $Z$ and rewired bonds, resembling the small-world network proposed
recently but with site-energy disorder and quantum links instead of classical
ones. The random rewiring of bonds in the chain with large $Z$ enhances both
the topological disorder and the effective dimensionality. From the competition
between disorder and dimensionality enhancement a transition from localization
to delocalization is found by using the level statistics method combined with
the finite-size scaling analysis. The critical value of the rewiring rate for
this transition is determined numerically. We obtain a universal critical
integrated distribution of level spacing $s$ in the form $I_{p_{c}}(s)\propto
\exp (-A_{c}s^{\alpha})$, with $A_{c}\simeq 1.50$ and $\alpha \simeq 1.0$. This
reveals the possible existence of metal-insulator transition in materials with
chains as the backbones.
