  We provide a method for the ranking of the reliability of two networks with
the same connectance. Our method is based on the Cheeger constant linking the
topological property of a network with its spectrum. We first analyze a set of
twisted rings with the same connectance and degree distribution, and obtain the
ranking of their reliability using their eigenvalue gaps. The results are
generalized to general networks using the method of rewiring. The success of
our ranking method is verified numerically for the IEEE57, the
Erd\H{o}s-R\'enyi, and the Small-World networks.
