复杂网络的顶点着色及其在疾病免疫中的应用  

Coloring the complex networks and its application for immunization strategy

作　　者：黄斌[1] 赵翔宇[2] 齐凯[2] 唐明[2,3] 都永海 

机构地区：[1]成都信息工程学院数学学院,成都610225 [2]电子科技大学互联网科学中心,成都610054 [3]韩国庆北国立大学数学系

出　　处：《物理学报》2013年第21期510-517,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11105025);博士后科学基金特别资助(批准号:2012T50711);博士后科学基金(批准号:20110491705);博士点新教师基金(批准号:20110185120021);中央高校基本科研业务费项目(批准号:ZYGX2011J056)资助的课题;韩国教育;科学与技术部支持的国家研究基金会基础科学研究项目(批准号:NRF-2013R1A1A2010067)的资助~~

摘　　要：在复杂网络研究中,对于网络结构特征的分析已经引起了人们的极大关注,而其中的网络着色问题却没有得到足够的重视.为了理解网络结构与着色之间的关系,本文研究了WS,BA网络以及不同宏观结构参量对于正常K色数的影响,发现最大团数可以大致反映正常K色数的变化趋势,而网络的平均度和匹配系数比异质性和聚类系数对于色数的影响更大.对于一些实际网络的正常着色验证了本文的分析结果.对复杂网络的顶点进行着色后,根据独立集内任意两个顶点均不相邻的特点,我们提出了基于独立集的免疫策略.与全网随机免疫相比,基于独立集的免疫策略可令网络更为脆弱,从而有效抑制疾病的传播.基于网络着色的独立集提供了一种崭新的免疫思路,作为一个简单而适用的平台,有助于设计更为有效的免疫策略.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.

关 键 词：复杂网络 正常着色 独立集 免疫策略 

分 类 号：R392.1[医药卫生—免疫学] O157.5[医药卫生—基础医学]