Blockchain and distributed ledger systems are pretty much natural targets of network science. They are based on networks regarding both the infrastructure and the transaction graph networks. On top most current network are public, meaning there is a really huge number of data available for analysis. Network science investigations could be carried out on two or three level.
1. On the infrastructure side, analysis of the P2P topology combining with the changing of the topology and consensus mechanism that can be analyzed. Some consensus mechanisms like Ripple or from Stellar are very much dependent on the network structure. Other classical algorithms like proof of work are perhaps less sensible, however certain network structures make different attacks vectors easier, whilst others guarantee almost the theoretical limits of Byzanzine fault tolerance.
2. On the transaction side, the dynamics of the different transactions which is important. This is theoretically similar to the cash-flow of the classical systems, the difference is here however that the dynamics of the transaction flow is much faster and all the information is public, implying a much broader investigation possibility.
3. Last but not least, the blockchain can be analyzed with the help of different other systems. Examples might be the correlation of the blockchain or the transaction flow of two blockchains and perhaps the exchange rates of the two cryptocurrencies. Another option might be to analyze the connections between a blockchain solution and a traditionally centralized www system.