## 5 Conclusions  
In this study, we looked for community structures and other network properties of return and volatility of global 24 stock market networks. First, we performing the detrended cross-correlation analysis (DCCA) for the return and volatility of the global 24 stock market composite price index time series for 1997-2016. We analyzed the time series divided into one year, four years, 10 years, and 20 years to see the dynamics of the network. Second, two markets are linked by considering that there is a strong correlation if the correlation coefficient of any two markets through DCCA exceeds the threshold value 0.7. Here, the threshold value 0.7 is the median of the general classification principle, strong correlation (0.6), and very strong correlation (0.8), which illustrates our analysis results well. Third, we applied the _Girvan-Newman method_ in the stock market networks to detect the community structure. Finally, we calculated macroscopic network properties and inferred the association with international economic events. Figures 5-7 show the dynamics of optimal community structures for the global 24 stock market networks using the _Girvan-Newman method_ for four-year, 10-year, and 20-year length time series. We can find important properties here. The community structure of return and volatility is similarly formed at each period, and the size of community grows to 2008-2012 (right after the global financial crisis triggered by USA and European fiscal crisis) and becomes smaller during the five periods. Therefore, we can infer that the global stock market cooperates in the event of a financial crisis and forms a huge community according to the _Girvan-Newman method_. The structures of the return and volatility are similarly formed. The stock market networks have a huge community that consists \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{**Period**} & \multirow{2}{*}{**Year**} & \multirow{2}{*}{\(\langle k\rangle\)} & \multirow{2}{*}{\(L\)} & \multirow{2}{*}{\(E^{\text{global}}\)} & \multirow{2}{*}{\(E^{\text{local}}\)} & \multirow{2}{*}{\(C\)} & \multicolumn{2}{c}{**Node of m ax \(c_{k}^{\text{between}}\)**} \\  & & & & & & & & **with Its Value** \\ \hline \multirow{6}{*}{return} & \multirow{6}{*}{4 years} & 1997-2000 & 1.250 & 1.812 & 0.079 & 0.361 & 0.866 & USA2 & 0.055 \\  & & 2001-2004 & 3.416 & 1.327 & 0.178 & 0.385 & 0.794 & USA3 & 0.036 \\  & & 2005-2008 & 5.916 & **1.888** & 0.411 & 0.558 & 0.728 & Korea1 & 0.130 \\  & & 2009-2012 & **6.750** & 1.726 & **0.473** & **0.620** & 0.787 & Hong Kong & 0.157 \\  & & 2013-2016 & 1.416 & 1.566 & 0.082 & 0.295 & **0.791** & Netherland & 0.024 \\ \cline{2-10}  & \multirow{2}{*}{10 years} & 1997-2006 & 2.083 & 1.553 & 0.128 & 0.327 & 0.791 & UK & 0.035 \\  & & 2007-2016 & 10.500 & 1.447 & 0.602 & 0.805 & 0.842 & Korea1 & 0.069 \\ \cline{2-10}  & \multirow{2}{*}{20 years} & 1997-2016 & 4.833 & 1.737 & 0.341 & 0.508 & 0.785 & Hong Kong & 0.123 \\ \hline \multirow{6}{*}{volatility} & \multirow{6}{*}{4 years} & 1997-2000 & 0.833 & 1.230 & 0.041 & 0.222 & 0.761 & France & 0.008 \\  & & 2001-2004 & 1.583 & 1.379 & 0.086 & 0.300 & 0.808 & USA1 & 0.013 \\ \cline{1-1}  & & 2005-2008 & **11.083** & 1.380 & **0.619** & **0.814** & **0.862** & Netherland & 0.063 \\ \cline{1-1}  & & 2009-2012 & 5.000 & **1.921** & 0.360 & 0.541 & 0.698 & Korea1 & 0.165 \\ \cline{1-1}  & & 2013-2016 & 1.833 & 1.578 & 0.105 & 0.341 & 0.822 & USA1 & 0.024 \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{10 years} & 1997-2006 & 1.667 & 1.310 & 0.088 & 0.268 & 0.881 & USA2 & 0.028 \\ \cline{1-1}  & & 2007-2016 & 17.083 & 1.112 & 0.789 & 0.880 & 0.921 & Netherland & 0.008 \\ \cline{1-1} \cline{2-10}  & \multirow{2}{*}{20 years} & 1997-2016 & 6.833 & 1.818 & 0.542 & 0.661 & 0.752 & Hong Kong & 0.260 \\ \hline \hline \end{tabular}
\end{table}