Importance-based entropy measures of complex networks' robustness to attacks

Intentional attacks usually cause greater damage than random failures to complex networks, so it is important to study the networks' resilience to attacks. Although various entropy measures have been available to measure the heterogeneity of complex networks to analyze their properties, they can not distinguish the difference of robustness between the scale-free networks and random networks. Hence, we propose a new entropy measurement base on the node importance to measure complex networks' robustness to attacks. The experimental analysis shows that the importance-based entropy measure describes the robustness properties of complex networks precisely which are in consistent with the well-known conclusion and it distinguishes the difference between the scale-free networks and random networks more obviously in the view of robustness than the existing entropy measures in the view of heterogeneity. We conclude that the entropy measurement based on the node importance is an effective measure of network's resilience to intentional attacks and heterogeneity is not in direct relationship with the network's resilience to errors and attacks for any network.