More about this chart. Explanation. The number of daily confirmed transactions highlights the value of the Bitcoin network as a way to securely transfer funds.
Table of contents
- How does Bitcoin work?
- Bitcoin Average Transaction Fee
- Quantitative Analysis of the Full Bitcoin Transaction Graph | SpringerLink
- Bitcoin in Various Currencies
In the transaction graph of a cryptocurrency, vertices are accounts or addresses in the currency network, and the edges between them are transactions between those accounts. Since these accounts have hidden identities, they do not represent the true identities of individuals. Note that a person can create multiple accounts, and it is almost impossible to link these accounts, and detect that they belong to the same individual.
There are graph analytics methods and heuristics to link some of the accounts Nick , but since these techniques are prone to errors and cannot detect all related accounts, we do not use any of these methods for linking accounts and merging their corresponding nodes in the transaction graph. Our contributions can be summarized as follows:. We compare the structural properties of the transaction graphs of five widely-used cryptocurrencies.
We discuss the relation between the transaction graph properties with technical aspects and historical events of each coin. We investigate the evolution of the transaction graph over time and study the effect of supply and demand, and price of each coin on the transaction graph. Various studies have been conducted on cryptocurrency transaction networks from different perspectives. Among these studies, there is no comprehensive review, and most of them have focused on one or two specific coins, especially Bitcoin and Ethereum, and used outdated blockchain data which does not cover recent developments in the field.
In most of these studies the transaction graph is investigated statically and its dynamics and evolution over time are not considered. We have categorized related work by the cryptocurrencies they have reviewed:. Ron and Shamir in , analyzed the bitcoin transaction graph statically.
In another study on Bitcoin, Maesa et al. They analyzed the distances between nodes and studied graph metrics such as density and phenomena like the rich-get-richer phenomenon Di Francesco Maesa et al. But these studies are only limited to Bitcoin, and with modern wallets and the advent of mixers Mixing service , the deanonymization heuristic has become ineffective.
How does Bitcoin work?
In another related work by Fleder et al. Their analysis and calculations on the transaction graph is limited, and their deanonymization heuristic is no longer valid due to the existence of mixers. Kondor et al. In a study by Chen et al.
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They did not examine the money flow graph dynamically and also their study is limited to a few metrics. In another study by Guo et al. However, this study only deals with a small part of the blockchain at two specific time spots and is not showing the dynamics of the graph over time Guo et al. Liang et al. Currently, Namecoin is no longer active and it is not in the list of top coins according to their market capitalization CoinMarketCap Furthermore, their study is not as comprehensive as ours and they focused on a few metrics and a limited number of cryptocurrencies.
The data used in this study were obtained directly from the blockchain of the cryptocurrencies. There are several ways to get these information, and we used two different methods for data collection. For Bitcoin, Ethereum, Litecoin, and Dash, we obtained blockchain data from their peer-to-peer network using their client software. These data are stored in binary format and needed to be converted into human-readable formats such as comma-separated values CSV for further analysis.
These binary data can be converted by parsers which output several large CSV files. These files contain each transaction details including the timestamp, the number of inputs and outputs of the transaction, the incoming and outgoing addresses, and other related information which is stored in the blockchain. We also made a custom parser for parsing Dash blockchain. To build the transaction graph, we need database operations like Join and Select. Due to the high volume of data, we used Apache Spark , which is one of the most well-known big data processing tools, to perform these operations ApacheSpark The blockchain structure for each of these cryptocurrencies is different, but some are very similar.
For example, the Bitcoin and Litecoin blockchains are very similar, but the Ethereum blockchain has a completely different structure because of its nature and sophistication.
But in all of them, the transaction information is contained within the blocks. In each block, a certain number of transactions can be placed. In general, blockchains can be divided into two categories: UTXO Unspent transaction output -based and account-based. In the UTXO-based blockchains, each transaction input is linked to an output of a previous transaction. In other words, current transactions in a block are spending the outputs of previous transactions and generating new outputs to be spent in subsequent transactions.
In the outputs of the transactions, the addresses to which the output values belong are placed. But in the account-based blockchains, the addresses of the incoming and outgoing accounts are explicitly stated. But in Ethereum, whose blockchain is account-based, each transaction has only one input and one output. In a transaction graph, nodes are accounts addresses, and the edges are the transactions between these accounts. In this study, we considere a transaction graph as an unweighted undirected graph, but in some analyses, we use a directed version of that graph. Given that each block of the blockchain has a timestamp, we have divided the timeline into monthly intervals and created a transaction graph for each month that only includes the transactions in the blocks of that month.
To make a transaction graph from a set of transactions, we place one edge from each input address and to each output address in transactions in the graph. For Coinbase transactions, that include the block generation reward given to the miners and the inputs do not refer to a previous transaction outputs, we considered a supernode as its input and one edge of that supernode to each miner address. For example, in Fig. Generation of a transaction graph. There are various metrics for quantitative comparison between transaction graphs of different cryptocurrencies.
As mentioned earlier, the transaction graph can be viewed as a social network graph, and all metrics that can be calculated on social networks can also be studied for the transaction graph. We use the most common metrics that are meaningful in the context of transaction graphs and has a relation with technical details and historical events in the timeline of each coin.
Given the large size of these gigantic graphs, we only investigate the metrics that might be calculated in an acceptable period of time. In what follows, we introduce the metrics that are calculated on the cryptocurrencies transaction graph in this study. Clustering coefficient shows the tendency of graph vertices to create a cluster with other vertices in the graph, and is defined as:. A triad is a set of 3 nodes that at least two pairs of them are connected.
Since calculating the exact value of the clustering coefficient is hard in large graphs, we used an approximate method. In this method, instead of counting all triangles and triads, we randomly selected a specific number of triads and check that is it triangle or not. The estimated clustering coefficient was the percentage of triads that they were also a triangle. As the number of randomly selected triads increases, the estimated clustering coefficient will be closer to the exact value.
Density of an undirected graph with node set V and edge set E is defined as:. Edge-to-vertex ratio is calculated by dividing the number of edges of a graph to the number of its vertices. Size of maximum clique in a graph is the number of vertices of its largest complete subgraph.
A complete subgraph is a set of nodes and edges in a graph where every pair of nodes is connected by an edge Diestel The assortativity coefficient of a graph indicates the tendency of the graph vertices to attach to other vertices that are similar to them. The similarity of two nodes is usually measured by their degrees, and the assortativity coefficient is calculated by the Pearson correlation coefficient of degree between pairs of linked nodes. The value of 1 indicates that the graph is perfectly assortative and the vertices tend to have an edge with other vertices of similar degree.
The repetition ratio in the transaction graph indicates the percentage of repetitive nodes or edges in the MTG in a month compared to the previous month. Since the repetition ratio for each month is calculated using to the previous month MTG, the repetition ratio for the first month is not defined.
The relative growth rate RGR in the interval [ t 1 , t 2 ] is calculated using the following equation:.
Bitcoin Average Transaction Fee
In this section we present the results of our comprehensive investigation on cryptocurrencies transaction graph. Because of the large volume of the extracted graphs, we need high computational power and memory to store them and perform calculations on them. Figures 2 a and b illustrate the number of edges and the number of nodes in the MTG graph, respectively.
Alongside these curves, the Bitcoin price is also included for comparison. For a closer look, we obtained the price of all the coins under review from CoinMarketCap CoinMarketCap , and for each coin, we measured the correlation between its price and the size of its MTG graph. In particular, this relationship is very strong in Bitcoin, Litecoin and Ethereum.
Quantitative Analysis of the Full Bitcoin Transaction Graph | SpringerLink
The plot of the number of edges and the number of nodes in the CMTG graph over time is shown in Figs. As expected, these charts are monotonically increasing due to the cumulative nature of the CMTG graph and shows the growth rate of the CMTG graph of each cryptocurrency over time. In these charts, it can be seen that at some points, the charts intersect, indicating that the number of addresses and transactions of the two currencies is identical and at certain points in time. For example, late in the year and early in the year , due to the steep rise in the number of addresses of Ethereum, the number of Ethereum addresses exceeded Litecoin and Dash.
The reason is that Ethereum has attracted many users by introducing new and unique features such as smart contracts in a short period.
Bitcoin in Various Currencies
The chart also shows that at the beginning of the year , Ethereum has the second largest number of addresses after Bitcoin. To be more specific, we calculated the relative growth rate RGR for the number of edges and nodes of the CMTG graph from the start of each cryptocurrency until the end of our study, the results of which are presented in Table 2. As can be seen, Ethereum has the highest growth rate for both number of edges and number of nodes among the five cryptocurrencies. Another metric we examined for cryptocurrencies transaction graphs is the density of these graphs.
In Figs. As can be seen in Fig. This trough created in the density of the MTG graphs coincides with the price peak happened for Bitcoin. To be more precise, for each coin we measured the correlation of price with the density of its MTG graph. Table 3 shows that for all the currencies, there is a negative correlation between the density of the MTG graph and the price of that currency. This negative correlation is especially strong in Bitcoin, Litecoin, and Dash. Density of transactions graphs over time.
The reason for this can be justified by the fact that to remain anonymous, each user usually generates a new address for a new transaction, and by receiving money from one of the existing addresses, a new edge is created in the transaction graph, thus for each transaction one edge and one node is added to the transaction graph, which results in a linear increase in the number of edges relative to the number of nodes, thereby reducing the graph density. In the early months, due to the steady rise in the price of coins, we are seeing an increase in users willing to invest in the cryptocurrencies market, and as a result, there is an increase in the number of new addresses in these coins, which in turn reduces the density of the transaction graph.
In Fig. This implicitly indicates that the number of new Ethereum accounts is increasing sharply, resulting in a decrease in the density. After observing the growth trend of edges and nodes of the CMTG, the next experiment was to determine whether the number of edges of this graph grow linearly with respect to its number of nodes. For this study, we assumed that the number of graph edges is a power function of the number of nodes:. We estimated the parameters a and b for each of the coins studied.
For this purpose, we applied goodness-of-fit tests on the number of edges and the number of nodes in the CMTG graph in different months, we calculated the best curve available by finding the most appropriate a and b for each coin. As shown in Fig. This measure indicates how well points fitted the curve.