This study aims to explore the dependencies on the cryptocurrency market using social network tools. We focus on the correlations observed in the cryptocurrency returns. Based on the sample of cryptocurrencies listed between January 2015 and December 2022 we examine which cryptos are central to the overall market and how often major players change. Static network analysis based on the whole sample shows that the network consists of several communities strongly connected and central, as well as a few that are disconnected and peripheral. Such a structure of the network implies high systemic risk. The day-by-day snapshots show that the network evolves rapidly. We construct the ranking of major cryptos based on centrality measures utilizing the TOPSIS method. We find that when single measures are considered, Bitcoin seems to have lost its first-mover advantage in late 2016. However, in the overall ranking, it still appears among the top positions. The collapse of any of the cryptocurrencies from the top of the rankings poses a serious threat to the entire market.