## 5 Conclusions

Table 3: Network properties of global 24 stock markets generated by DCCA methodology of Europe (France, Germany, Netherland, UK), USA (USA1, USA2, USA3, USA4), and Oceania (Australia1, Australia2) for 2001-2004, 2005-2008, and 2009-2012 for four-year length time series (Figure 5c-h). Additionally, several small communities were found in 1997-2000 and 2013-2016 (Figure 5a,b,i,h). The dynamics of community structures from 1997 to 2016 partitioned by 10 years does not change the characteristics. The communities are enlarged for the post decade (2007-2016) compared to the prior decade (1997-2006) and the size of communities of volatility is larger than that of return (Figure 6). [PERSON] et al. [18] analyzed 20 stock markets for subprime crisis. In these results, three groups were found: (Europe), (America), and (Asia, Australia) in the pre-subprime crisis period. In the post-subprime crisis period, two groups of (Europe, America) and (Asia, Australia) are detected. They found the characteristics of the formation of large-scaled intercontinental solidarity after the financial crisis. We found a similar property in this study. Figure 6 shows the solidarities of pre-subprime crisis. Figure 6a shows three groups: (Europe, America), (South America), and (Asia), In Figure 6b, two groups are detected: (Europe, USA) and (Australia). On the other hand, during the post-subprime crisis period, most of the stock markets formed a huge network. We analyzed 24 stock markets instead of 20 in [PERSON] et al. [18]. Comparing and analyzing the global stock market structure from the community perspective with their research, we can see the similar result that the structure is different before the financial crisis, but it has a huge community after the financial crisis. On the other hand, in the 20-year length time series, the community structure for the whole period can be seen as one picture, it is commonly making a community that consists of Europe, USA, and Oceania in return and volatility (Figure 7). Table 2 shows the detailed list of community. Additionally, we inferred macroscopic properties of the global stock market networks by calculating average degree \(\langle k\rangle\), characteristic path length \(L\), global efficiency \(E^{\text{global}}\), local efficiency \(E^{\text{local}}\), clustering coefficient \(C\), and modularity \(Q\) in Equations (6)-(13) (Figure 8). The remaining five properties have similar values of return and volatility, except for modularity \(Q\). In conclusion, we found that there was no superiority between return and volatility in network analysis. We were able to catch the events that Asian liquidity crisis in 1997, world-wide dot-com bubble collapse in 2001, global financial crisis triggered by USA in 2008, European sovereign debt crisis in 2010, and Chinese stock price plunge in 2015. [PERSON] et al. [16] confirmed that the modularity value temporarily plummeted during the black Monday crisis. On the other hand, [PERSON] et al. [17] showed that the \(E^{\text{global}}\) value increased before the subprime crisis and rapidly decreased during the crisis in the SSE (Shanghai Stock Exchange) network. Both studies show that the network property value increases or decreases rapidly and sensitively responds to the financial crisis. In this paper, we confirmed that \(\langle k\rangle\), \(E^{\text{global}}\) and \(E^{\text{local}}\) are related to the financial crisis. Thus, the network properties are candidate indicators for predicting global financial market trends. However, such singularities have not been obtained for other network properties. In addition, no scientific reason has been found as to whether the three properties \(\langle k\rangle\), \(E^{\text{global}}\), and \(E^{\text{local}}\) are related to the financial crisis. In future studies, stock market data from a wider variety of countries will be needed to derive results that reflect reality. Moreover, we would like to construct a weighted network according to the magnitude of correlation coefficient of DCCA.