A invulnerability assessment based on importance-degree of node for weighted network under attack with partial information

We study invulnerability of complex networks subject to attacks on nodes and links. For the purpose of precisely assessing invulnerability of complex networks, in this paper we proposed an invulnerability assessment on the basis of importance-degree and partial attack information by measuring two metrics of network invulnerability, robustness and efficiency. We defined the term of importance-degree to describe importance of different nodes in the networks. We form a probability model to describe the process of acquiring information under three types of attacks, random attacks, partial information attacks and intentional attacks, and simulate the process of acquiring partial information by sampling nodes in accordance with the probability model. The simulation results contain that weighted networks hold strong invulnerability to random attacks, whereas they are extremely fragile when suffering those intentional attacks; more information is exposed, less invulnerability networks display, especially complete information attacks which are the same with intentional attacks that all information of nodes or links would be acquired by assailants; the more important information is acquired, the more quickly network invulnerability decreases. This conclusion can guide people to implement corresponding protection strategy of hiding important information based on the importance-degree of nodes.