Analysis Of The Shanghai Composite Index Sery Based On Complex Network Analysis

Research on The Stock Market Law is more and more popular.The reasons are include two aspects:On one hand,Investors want to find some Market Rules which are helpful to their Investment.On the other hand,Scholars study some theories based on the data of the Stock Market.But most of these studies are based on the relationships of some stocks.In this paper,We try to explore the rule of the wave of the Shanghai Composite Index from a new standpoint:Complex Networks.Through Coarse Graining method,We transfer the Close Price of the Shanghai Composite Index in to a symbol sery which includes five characters{R,r,e,D,d}.Two continuous symbols are combined in to a wave mode which is considered as the node of the network.Then we connext these nodes in chronological order and create a directed and weighted network.Then we compute some dynamical statistics such as degree and the degree distribution,the length of the shortest path,clustering coefficient and betweenness centrality and so on so that we can study the topological structure of the network.On the other hand,with clustering analysis method of the Data Mining,We group these nodes in to some clusters, and these nodes in one cluster are considered as a new node.Then we reconstruct the network and get more useful information from the wave process of the Shanghai Composite Index.In our study,we know that the fluctuation of the Shanghai Composite Index are in complexity and are similar to chaotic characteristics,and are not totally random.In the network The small-fluctuation-mode have high centralization and they are in the favored position.This conclusion is consistent with the market discipline.As we all known,no matter the bull market,bear market or the horizontal price movement,small fluctuations are need to adjust the market.Otherwise,the transfer of the other big-fluctuation modes can offer investors much more useful information.