Using topological characteristics to evaluate complex network models can be misleading

TL;DR

Evaluating complex network models solely on traditional topological metrics can be misleading, as such metrics do not necessarily reflect the network's robustness and real-world performance.

Contribution

This paper demonstrates that common topological metrics are insufficient for accurately assessing the realism of network models, especially regarding robustness.

Findings

Topological metrics can be misleading in model evaluation.

Models may match topological features but differ significantly in robustness.

Current metrics do not reliably predict network resilience.

Abstract

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.