This paper aims to analyse the connectivity of 13 stock markets, between 1998 and 2019, with a time-varying proposal, to evaluate evolution of the linkage between these markets over time. To do so, we propose to use a network built based on the correlation coefficients from the Detrended Cross-Correlation Analysis, using a sliding windows approach. Besides allowing for analysis over time, our approach also enables us to verify how the network behaves for different time scales, which enriches the analysis. We use two different properties of networks: global efficiency and average grade, to measure the network’s connectivity over time. We find that the markets under analysis became more connected before the subprime crisis, with this behavior extending even after the Eurozone crisis, showing that during extreme events there is an increase in financial risk, as found in the international literature.