Table 1.
Summary of cryptocurrencies studied in this paper.
Fig 1.
Illustration of transaction network construction.
(A) An example of Bitcoin transaction details. (B) Example information extracted from Bitcoin transactions, and the information in the orange box correspond to the transaction in (A). (C) The Bitcoin transaction network as a directed graph.
Fig 2.
The size of accumulated transaction networks with respect to various cryptocurrencies in log coordinate.
The number of nodes and edges are used to represent the size of networks. The three networks have similar growth pattern with rapid growth first and slower growth later.
Fig 3.
The average node degree of accumulated networks over time.
The average degree of the three networks is not constant.
Fig 4.
The number of edges e(t) versus the number of nodes n(t) in accumulated transaction networks in log coordinate.
The red lines show fitted power-law distribution for the networks. In the figure’s equation, x represents the number of nodes and represents the fitting number of edges, and the exponents are 1.15, 1.00, 1.05, respectively.
Table 2.
Fitting parameters of the power law.
Fig 5.
Monthly repetition ratios over time.
(A) The ratios of edges. (B) The ratios of nodes. After the initial phase, all ratios reach relatively low values.
Fig 6.
Samples of degree distributions of monthly networks.
Data are sampled from Bitcoin (top row), Ethereum (middle row), and Namecoin (bottom row). Example data for power-law fitting are approximate fit (first column), poor fit (medium column), and inconsistent fit (last column). The legends show the fitting exponent γ in p(k) ∼ k−γ with respect to indegree and outdegree distribution.
Fig 7.
Evolution of the degree assortativity.
In the figure of Bitcoin, we magnify the y-axis of the data in the yellow box and display it in the bottom right corner. After the initial phase, the coefficients of Bitcoin and Ethereum are negative, and the coefficient of Namecoin converges to a certain range near 0.
Fig 8.
A comparison of the average degree of nodes’ neighbors and the degree of nodes.
The red line indicates the degree of the node and the average degree of the node’s neighbors is equal. In networks without degree correlations, the 〈knn〉 is constant. However, for Bitcoin and Ethereum, 〈knn〉 is a decreasing function, while for Namecoin 〈knn〉 is not.
Fig 9.
Evolution of clustering coefficients.
If the average clustering coefficient of a network is rather higher than a random network with the same degree sequence, the network is a small-world network. In the figure of Bitcoin, we magnify the y-axis of the data in the red box and display it in the upper right corner. We find only Bitcoin exhibits this feature.
Fig 10.
The relative size (blue line) is the proportion of LCC nodes in all nodes, and the diameter (green line) reflects the connectivity of the LCC. Later stage, the relative sizes of the three networks are 60%, 40% and 5% respectively, and the diameter of BTC is 100, while the other two are in fluctuations.