Abstract
It is a very important issue to understand exactly the mechanism of the collapse of the giant component in a complex network caused by various types of node removal in order to build up robust networks under a wide range of external disturbances in the real world. In most existing theoretical analyses, however, the structure of networks under consideration is specified only by their degree distribution and the degree-degree correlation between nodes, which is not necessarily small in real-world networks, has not been incorporated. In this article, we study using analytical method the mechanism of the collapse of the giant component in a complex network under the influence of various ways of node removal. The degree-degree correlation is incorporated in the first place of the analysis. Though the derived equations are valid for any types of node removal, we show in this article the results for two specific cases of node removals; the one is random node removal with a given probability and the other is selective node removal in which the highly connected nodes (hubs) are selectively removed. From the results, we find that the networks with assortative degree-degree correlation where the nodes of the same degree tend to connect to each other becomes much more robust against both types of node removal than the networks with the same degree distribution but without any kind of degree-degree correlation. For scale-free networks, in particular, the robustness enhancement effect due to assortative degree-degree correlation is significant and the inherent vulnerability of the scale-free network against selective node removal is considerably improved by introducing assortative degree-degree correlations.
