The adverse effects of the high-power energy consumption by cryptocurrencies on the environment and sustainability have raised the interest of a large body of policymakers and market participants. We apply a network approach to investigate the dependency across clean energy, green markets, and cryptocurrencies from 1 January 2018 to 30 November 2021. Our results indicate that sustainable investments, particularly DJSI and ESGL, play a pivotal role in the network system during the COVID-19 crisis. We find that green bonds are the least integrated with the other financial markets, suggesting their significant role in providing diversification benefits to investors. Rolling windows estimation shows that the dependency across the examined marked increased sharply during the COVID-19 crisis, especially between March 2020 and March 2021, after which it faded and became weak and stable until the end of the sample period. Results of the centrality network are consistent with the dependency network analysis. \textcopyright 2023