  Graphical models are frequently used to represent topological structures of
various complex networks. Current criteria to assess different models of a
network mainly rely on how close a model matches the network in terms of
topological characteristics. Typical topological metrics are clustering
coefficient, distance distribution, the largest eigenvalue of the adjacency
matrix, and the gap between the first and the second largest eigenvalues, which
are widely used to evaluate and compare different models of a network. In this
paper, we show that evaluating complex network models based on the current
topological metrics can be quite misleading. Taking several models of the
AS-level Internet as examples, we show that although a model seems to be good
to describe the Internet in terms of the aforementioned topological
characteristics, it is far from being realistic to represent the real Internet
in performances such as robustness in resisting intentional attacks and traffic
load distributions. We further show that it is not useful to assess network
models by examining some topological characteristics such as clustering
coefficient and distance distribution, if robustness of the Internet against
random node removals is the only concern. Our findings shed new lights on how
to reasonably evaluate different models of a network, not only the Internet but
also other types of complex networks.
