We employ graph-based methods to examine the connectedness between cryptocurrencies of different market caps over time. By applying denoising and detrending techniques inherited from Random Matrix Theory and the concept of the so-called Market Component, we are able to extract new insights from historical return and volatility time series. Notably, our analysis reveals that changes in volatility-based network structure can be used to identify major events that have, in turn, impacted the cryptocurrency market. Additionally, we find that these structures reflect investors’ sentiments, including emotions like fear and greed. Using metrics such as PageRank, we discover that certain minor coins unexpectedly exert a disproportionate influence on the market, while the largest cryptocurrencies such as BTC and ETH seem less influential. We suggest that our findings have practical implications for investors in different ways: Firstly, helping them to avoid major market disruptions such as crashes, to safeguard their investments, and to capitalize on opportunities for high returns; Secondly, sharpening and optimizing the portfolios thanks to the understanding of cryptocurrencies’ connectedness.