Brittleness analysis and important nodes discovery in large time-evolving complex networks

The brittleness analysis and important nodes detection have been a hot spot in the complex networks. How to get the overall feature of the whole network and how to find out some important nodes are requisites to solve these problems. In this paper, we adopt the trace of the adjacency matrix and the centrality of the complex networks to give a quantitative and qualitative analysis of networks being studied. Results show that the k-shell plays a more important role than the degree centrality and the betweenness in finding important nodes, and it can also be used to give direction on the immunization and maintenance of complex networks.