建立了上市公司与其主要股东的关联网络,利用实际数据分析了中国股市2001到2010年的总体走势,证明了该网络属于典型的无标度网络,无标度指数的变化显示出从2006年开始上市公司中出现少数度值极大的in—hub节点,而上市公司的主要股东中出现了相对较多的out—hub节点.同时采用加权派系过滤算法分析了网络中3-派系(3-clique)下的社团结构,证实了从2006年开始一些大型国有企业上市后迅速地成为了网络中的核心节点,造成了网络资源重组现象.这同时解释了无标度指数的变化原因.然后通过研究近年来大公司之间的大额投资关系发现:这些大公司不但经历住了全球经济危机的考验,而且上市公司与大型控股公司之间的关系变得更加紧密.分别分析了该网络遇到随机故障和蓄意攻击时的稳健性.其中2008年中国受国际经济危机的影响正好与网络出现随机故障的情况类似,分析表明此时中国股市表现出强健的鲁棒性;但若对整个网络进行蓄意攻击,网络则明显表现出极强的脆弱性.
Firstly establish the correlated networks of the stock ownership structure and then investigate the overall trends of the stock markets in China during the period from 2001 to 2010, prove that such networks are typical scale-free networks, analyze the meaning of the fluctuation of the scale-free indices. We find out the 3-clique-communities of the correlated networks by the weighted clique percolation method (denoted as CFMw), which further provide the factual base for the changes of the scale-free indexes, then the core mutual investment relationship between the large or medium-sized state-owned listed companies and their holding enterprisers are researched by the removal method, which we find that the core mutual investment relationship after undergoing the sudden increase of the resource in 2007 and the economic crisis in 2008. Finally the static robustness of the networks has been researched. The worldwide economic crisis is just the example of the networks meeting the random failures. The results show that the Chinese stock markets have good robustness against the random failures. However, the networks show the obviously vulnerability if the networks meet intentional error or attack.