Analysis On Chinese Growth Enterprises Index Based On Complex Network

Chinese Growth Enterprises index is the barometer of Chinese Growth Enterprises market, this study analyzes the Chinese Growth Enterprises index from complex network view,it have innovative methods and ideas in this study.Firstly, Convert the Chinese Growth Enterprises index into network through visibility graph method and compared with Shenzhen Small and medium-size Enterprises index and Shenzhen Component Index in the same time period, from the perspectives of networks' scale-free, small world, fractal and hierarchical characters reveals the motion of time series. The results indicate that the visibility graphs of the three indexes are scale-free networks and the relationship between time series' Hurst index and power exponent of visibility graph show that the movement of Chinese Growth Enterprises index couldn't be depicted as fractal brown motion, while the movement of Shenzhen Small and medium-size Enterprises index and Shenzhen Component Index can be seen as fractal brown motion.Three time series' visibility graphs are all small world networks, among them, Chinese Growth Enterprises index have the strongest variability and small world network effect. All the three time series' visibility graphs are not fractal graphs due to the large assortative coefficients which means Hub nodes' strong connectivity.The hierarchy character of the visibility graph means the wave-like motion of time series, Chinese Growth Enterprises index has nearly the same hierarchy character with the other two indexes, which means they may have the same wave-like motion character.Secondly, Through Coarse Graining method, Chinese Growth Enterprises index was transformed into symbolic sequences. Symbols are combined into fluctuation modes, which are defined as the nodes of the network, and the transitions between these modes were considered as the links of the network, so Chinese Growth Enterprises index fluctuation network is a directed and weighted network, the network's topologic properties were analyzed form the complex network view.Research shows that the strength of the nodes is not uniform, some nodes have very large strength, these nodes were considered as the core modes.The Chinese Growth Enterprises index fluctuation network is a small world network, the average conversion days between modes is short. The assortative coefficients and centrality show that core modes switch frequently between each other, small number of the nodes undertake most of the network's betweenness centrality, these transit modes are mostly consisted of the core modes. Form the community perspect,some modes switch frequently between each other.Lastly, Using Chinese Growth Enterprises index trading volume information, index and its trade volume are combined into modes, through transitions between these modes, the index-volume network was built and research index-volume relation form complex network view. The results indicate that index price and volume usually change in the same direction and have some continuity, the distribution of edge and node is quite uneven. Topology analysis of the network show that the average conversion days between modes only need 1.4 days, index-volume network is a heterogeneous network, frequent modes usually change through infrequent modes. By measuring network's centrality, a small amount of nodes play the role of core and hub.