Coloring the complex networks and its application for immunization strategy

Structural analysis of complex networks has gained more and more concerns, but not enough attention has been paid to the coloring problem in complex networks. In order to understand the relationship between network structure and coloring problem, we investigate the effects of WS, BA networks and different macro-scale parameters on the K-proper coloring. We find that the maximum clique number can generally reflect the trend of K value change, the average degree and the degree correlation have a greater impact on the K value than the heterogeneity and the clustering coefficient. These results are verified on some real-world networks. After coloring the complex networks properly, the independent sets of networks can be obtained. According to the characteristic that any two vertices are not connected in an independent set, we propose a random immunization strategy based on the independent set. Compared with the random immunization, the proposed strategy can make the network more vulnerable, and thus effectively mitigate epidemic spreading. This immunization strategy is simple and practical, which helps to design more efficient immunization strategy.