Fig 1.
The data pipeline.
Fig 2.
The four degree distributions in 2011: (a) in-degree weighted by activity, (b) in-degree weighted by value, (c) out-degree weighted by activity, and (d) out-degree weighted by value.
The observed degree refers to individual Bitcoin addresses, while the weights -value and activity- represent, respectively, the total amount transacted and the total number of transactions between two addresses over the course of a full year.
Fig 3.
The four degree distributions in 2023: (a) in-degree weighted by activity, (b) in-degree weighted by value, (c) out-degree weighted by activity, and (d) out-degree weighted by value.
The observed degree refers to individual Bitcoin addresses, while the weights -value and activity- represent, respectively, the total amount transacted and the total number of transactions between two addresses over the course of a full year.
Table 1.
Summary statistics of the network snapshots: number of addresses, edges and edge density from 2009 to 2016.
Table 2.
Summary statistics of the network snapshots: number of addresses, edges and edge density from 2017 to 2023.
Table 3.
Share of the Bitcoin volume and nodes considered when filtering out transactions with an annual cumulative value of less than 0.0001 BTC.
Fig 4.
(a) Average degree weighted by activity and value.
In this case, in- and out-degree averages are equal. (b) Gini coefficients of the four degree distributions.
Fig 5.
(a) Effect of the filter on Degree Assortativity and (b) Transitivity Coefficients, per year.
Fig 6.
(a) The Gini index of the size distribution of the Weakly and Strongly Connected Components.
This index measures the inequality in the size distribution of the connected components within the network, and shows that most of the addresses are part of a single giant component that dominates the system. (b) Shares of the in- and out-egdes controlled by the richest 1% of nodes in terms of in- and out-degree. This measures the proportion of all incoming and outgoing edges that are controlled by the top 1% of addresses based on their in-degree and out-degree. (c) The percentage of the richest 1% in terms of in- and out-degree that are present in the Largest Strongly Connected Component. This shows that the set of the most connected nodes is within the core of the network.
Fig 7.
(a) The evolution of rt(b) and ( b) rt(i) over time; rt(b) and rt(i) are defined as in Eq (6).
rt(b) represents the ratio between the average balance (in bitcoins) of the ten richest nodes and the average balance across the entire network, while rt(i) refers to the same ratio but based on in-degree. An increase in either metric indicates that the wealthiest nodes -whether in terms of balance or connectivity- are becoming richer or more connected relative to the rest of the network.
Fig 8.
(a) The evolution of Xb,t and ( b) Yi,t and maximum possible values over time; Xb,t and Yi,t are defined as in Eq (7).
A curve that falls below the theoretical maximum indicates a persistence of the richest nodes over time, meaning that the same entities tend to remain among the richest addresses in different periods.
Fig 9.
Evolution of the set of the richest nodes over time, (a) by balance and (b) in-degree.