Quantitative Analysis Of Cryptocurrencies Transaction Graph by Amir Pasha Motamed

Quantitative analysis of
cryptocurrencies transaction graph
Amir Pasha Motamed and Behnam Bahrak

Abstract
Cryptocurrencies as a new way of transferring assets and securing financial transactions
have gained popularity in recent years. Transactions in cryptocurrencies are publicly
available, hence, statistical studies on different aspects of these currencies are possible.
However, previous statistical analysis on cryptocurrencies transactions have been very
limited and mostly devoted to Bitcoin, with no comprehensive comparison between
these currencies. In this study, we intend to compare the transaction graph of Bitcoin,
Ethereum, Litecoin, Dash, and Z-Cash, with respect to the dynamics of their transaction
graphs over time, and discuss their properties. In particular, we observed that the
growth rate of the nodes and edges of the transaction graphs, and the density of these
graphs, are closely related to the price of these currencies. We also found that the
transaction graph of these currencies is non-assortative, i.e. addresses do not tend for
transact with a particular type of addresses of higher or lower degree, and the degree
sequence of their transaction graph follows the power law distribution.
Keywords: Cryptocurrency, Transaction graph, Graph analysis, Blockchain

Introduction
Cryptocurrencies have made it possible for a financial system to perform transactions
without the need for a centralized authority while keeping the transaction details and
money generation clear and publicly available. Despite this transparency, people’s iden-

tities are hidden, and they can transact anonymously. All transaction information of a
cryptocurrency is usually stored in a distributed public ledger, named blockchain. The
tasks of recording, updating, and maintaining the blockchain is the responsibility of net-

work users for each coin, whose identities are unknown, and rewards have been created
to provide them with sufficient incentives to do so, making the network up and running.
Although the system is running by anonymous people, due to computational infeasi-

bility of forging digital signatures and security of cryptography algorithms, transaction
alteration is almost impossible. This level of security is guaranteed by cryptographic
algorithms, and as long as these algorithms are secure, cryptocurrencies integrity is
protected.
Bitcoin is the first cryptocurrency created by an anonymous person or group of peo-

ple by the nickname Satoshi Nakamoto, which established a decentralized money transfer
system using blockchain (Nakamoto 2008). Subsequently, other cryptocurrencies, which
are usually referred to as altcoins, were created by adding more capabilities and offering
alternative design criteria. Ethereum was introduced by Vitalik Buterin in 2015 and is the
first blockchain-based distributed computing platform to consider the concept of exe-

cutable smart contracts (Buterin 2014). It is one of the most influential and widely-used
cryptocurrencies introduced after Bitcoin. Litecoin is also one of the earliest cryptocur-

rencies that is technically very similar to Bitcoin and has only slight differences with it
(Litecoin 2019). For example, Litecoin uses the Scrypt hash function instead of SHA256
for proof of work, and records transactions in the blockchain four times faster than Bit-

coin. Litecoin is created as a hard fork of Bitcoin, and has a separate blockchain. Dash
is another cryptocurrency which is quite similar to Bitcoin and uses the X11 hashing
algorithm for proof of work (Duffield and Diaz 2014). Similar to Litecoin, Dash has a sep-

arate blockchain, with transactions speed 4 times faster than Bitcoin. Z-Cash is a highly
secure cryptocurrency that uses zero-knowledge proofs, as a result of which privacy and
anonymity of users is significantly enhanced (Hopwood et al. 2018).
In all of the mentioned cryptocurrencies, the ability to transfer money is the basic
and common core capability. Using the blockchain data of each of these currencies, the
transactions in which they occur can be accessed. As a result, it is possible to analyze
transactions in these currencies from different aspects and perform a variety of statisti-

cal analyses on them. In particular, it is possible to examine a real network of financial
transactions for each cryptocurrency.
In this paper, the financial exchange network of the five aforementioned cryptocurren-

cies has been studied and several statistical metrics and network measures are calculated,
and their meanings are discussed. From a perspective, this financial exchange network
can be seen as a social network. In social networks, nodes are individuals, and the edges
between them can be friendships or other social relationships. 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 per-

son 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 2015), 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:
1 We compare the structural properties of the transaction graphs of five widely-used
cryptocurrencies.
2 We discuss the relation between the transaction graph properties with technical
aspects and historical events of each coin.
3 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.
Related work
Various studies have been conducted on cryptocurrency transaction networks from dif-

ferent 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:

Quantitative Analysis Of Cryptocurrencies Transaction Graph by Amir Pasha Motamed