Self-similarity research of stock networks

Complex network theory is a new approach to analysis stock problems. In this paper, the network is constructed as the following way: each stock is treated as node and the correlations of stock prices' fluctuation represent edges. After a suitable threshold is chosen, an adjacency metric is obtained. Based on the theories and methodology of complex networks, we discuss the degree distribution, average path length and clustering coefficient of the stock market network and the results show that the network exhibits small world effect and scale-free property. Furthermore, another important property self-similarity has been found with the following two methods: one is quantitatively analyzing nodes degree distribution with R/S theory to get the Hurst index of degree, the other is qualitatively analyzing and comparing volume dimension by average path length and clustering coefficient of network with Box Covering method.