Research on the Topology, Community and Robustness of the correlated networks of listed companies, funds and their main holders in China

We establish the correlated networks of the listed companies, funds and their main holders and find that such networks are typical scale-free networks. The scale-free indices of the In-degree assets and Out-degree assets of the vertices indicate that the vertices, which represent the super-scale companies newly listed on the stock markets in 2006 and 2007, not only make the networks resources´ re-arrangement, but also make the status of the previous In-hub vertices lower relatively. Then we study the 3-clique-communities of the networks by Directed Clique Percolation Method and the results are consistent with the fluctuations of scale-free indices. The super-scale companies newly listed on the stock markets can become the hub vertices quickly and strengthen the mutual investment relationships among the previous listed companies and funds. The large investment relationship between the large companies and their main holders are researched by removal method. We find that the mutual investment relationships among the large companies and funds are closer than the generally investments relationships every year, and the state-owned enterprises listing on the stock markets in 2006 and 2007 have succeeded to undergo the economic crisis and developed healthily. Finally, the robustness of the networks has been studied through three approaches, and the worldwide economic crisis is just the example of the random failure on the whole networks. The results show that the Chinese stock markets have good robustness at this condition. However, the networks show the obviously vulnerability if the stock markets meet the intentional attack.