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Listed energy company is the principal part of the energy market, including the energy investment, energy trade, energy operation etc.. Stockholders are the owners of the listed energy companies, whose relationships would affect the stability of the energy market directly. In order to analyze the evolution features and stability of the relationships between the stockholders, we constructed a generator holding-based structural equivalence network of the shareholders based on the primitive affiliation network of the listed companies and their shareholders. The main data used in this paper is the semi-annual reports from 2003 to 2012 which contain the information about Chinese listed energy companies' top 10 shareholders. The holding-based network takes the shareholders as the nodes, whether holding the same listed energy companies' stock at the same period as the edges, and the number of the listed energy companies holding at the same time as the weights. In this paper, we improved the traditional Heuristic method and then found the maximal connected sub-graphs of the holding-based networks in different time domain by the improved Heuristic method. The main method and theory used in this paper is complex network, we calculated and analyzed the evolution and the stability of the maximal connected sub-graphs. This paper comes up with a new angle to analyze the relationships in the energy stock market, and present a new method to analyze the stockholders' behaviors.

The data in this paper was collected from the semi-annual reports between 2003 and 2012 which disclosed the Chinese fund management companies' shareholdings in different listed companies. The holdings-based network of Chinese fund management companies is constructed by taking fund management companies as the nodes, the holding of stock of the same listed company at the same period as the edges, and the number of the listed companies holding at the same time as the weight of the edges. Based on the methods such as statistical physics, etc., the stability of the networks at different times is analyzed, and then the correlation of the holding behavior between the nodes with different topological characteristics and three different sets of nodes are calculated and analyzed. Three different sets are the set of nodes in the full graph with a given stock at t-1 (the first type of nodes), the set of nodes in the holing-based network without holding a given stock at t-1 (the second type of nodes), and the set of the new nodes which appear at t (the third type of nodes). The result shows as follows. Firstly, the correlation coefficient of the holding behavior between the node and the second type of nodes rises with the node clustering coefficient increasing; secondly, the node holding behavior is highly correlated with the second type of nodes and with the third type of nodes only when the values of the node average degree and strength are high; finally, the node holding behavior is not related to the third type of nodes at all. This paper propose a new method to study the correlation of stock market, and it is a basis for the further investigation on the structure equivalence network in stock market and also the differences of the importance between the nodes.