We investigate the price synchronization and reveal the dominant cryptocurrencies in the relevant market. For this, we use descriptive metrics and a novel methodology both from the area of Complex Networks. The study is conducted for three consecutive years, 2016, 2017, 2018. In doing so, the cross-correlation-based networks of the cryptocurrencies under examination are created and subsequently their properties for each year are analyzed and compared. The novel Threshold Weighted-Minimum Dominating Set (TW-MDS) methodology is employed in order to identify the so-called dominant cryptocurrencies for each year. In this framework, a node is identified as dominant when it can adequately describe the collective behavior of its relevant neighborhood. The empirical results provide strong evidence of an increased price synchronization. As a result, a well-constructed investment portfolio cannot include only or in large proportion cryptos of the same neighborhood. Another interesting finding is that, contrary to what may be expected, the cryptocurrencies that are identified as dominant are not always the most popular i.e., the ones with the highest capitalization (such as Bitcoin or Ethereum).