State and Network Structures of Stock Markets around the Global Financial Crisis

We consider the effects of the 2008 global financial crisis on the global stock market before, during, and after the crisis. We generate complex networks from a cross-correlation matrix such as the threshold network (TN) and the minimal spanning tree (MST). In the threshold network, we assign a threshold value by using the mean and standard deviation of cross-correlation coefficients. When the threshold is equal to the mean of these coefficients, we observe a giant cluster composed of three economic zones in all three periods. We find that during the crisis, the countries in the Asian zone were weakly connected and those in the American zone were tightly linked to the countries in the European zone. At a large threshold, the three economic zones were fragmented. The European countries connected tightly, but the Asian countries bound weakly. The MST constructed from the distance matrix. In the MST, France remained a hub node in all three periods. The size of the MST shrank slightly during the crisis. We observe a scaling relation between the network distance of nodes from the central hub (France) and the geometrical distance. We observe the topological change of the financial network structure during the global financial crisis. The TN and MST are complementary roles to understand the connecting structure of financial complex networks. The TN reveals to observe the clustering effects and robustness of the cluster during the financial crisis. The MST shows the central hub and connecting node among the economic zones.