Using the spillover index approach and its variants, we examine both static and dynamic volatility connectedness among eight typical cryptocurrencies. The results reveal that their connectedness fluctuates cyclically and has shown an obvious rise trend since the end of 2016. In the variance decomposition framework, we further construct a volatility connectedness network linking 52 cryptocurrencies using the LASSO-VAR for estimating high-dimensional VARs. We find that these 52 cryptocurrencies are tightly interconnected and “mega-cap” cryptocurrencies are more likely to propagate volatility shocks to others. However, some unnoticeable cryptocurrencies (e.g., Maidsafe Coin) are also significant net-transmitters of volatility connectedness and even have larger contribution of volatility spillovers to others. •Total connectedness of 8 cryptocurrencies fluctuates periodically and increases from end-2016 onwards.•Volatility connectedness network of 52 cryptocurrencies is built and analyzed.•The level of incoming or outgoing connectedness of a cryptocurrency is partly linked to its market cap.•Bitcoin is proved to be an important net-emitter of connectedness but not the dominant one.•Some unnoticeable cryptocurrencies (e.g., Maidsafe Coin) also transmit strong volatility shocks to others.