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The Anti-Social System Properties:
Bitcoin Network Data Analysis
Israa Alqassem, Iyad Rahwan and Davor Svetinovic, Senior Member, IEEE
Abstract—Bitcoin is a cryptocurrency and a decentralized
semi-anonymous peer-to-peer payment system in which the
transactions are verified by network nodes and recorded in a
public massively-replicated ledger called the blockchain. Bitcoin
is currently considered as one of the most disruptive technologies.
Bitcoin represents a paradox of opposing forces. On one hand,
it is fundamentally social, allowing people to transact in a
peer-to-peer manner to create and exchange value. On the
other hand, Bitcoin’s core design philosophy and user base
contain strong anti-social elements and constraints, emphasizing
anonymity, privacy and subversion of traditional centralized
financial systems. We believe that the success of Bitcoin, and the
financial ecosystem built around it, will likely rely on achieving
an optimal balance between these social and anti-social forces. To
elucidate the role of these forces, we analyze the evolution of the
entire Bitcoin transaction graph from its inception, and quantify
the evolution of its key structural properties. We observe that
despite its different nature, the Bitcoin transaction graph exhibits
many universal dynamics typical of social networks. However,
we also find that Bitcoin deviates in important ways due to
anonymity-seeking behavioral patterns of its users. As a result,
the network exhibits a two-orders-of-magnitude larger diameter,
sparse tree-like communities, and an overwhelming majority of
transitional or intermediate accounts with incoming and outgoing
edges but zero cumulative balances. These results illuminate the
evolutionary dynamics of the most popular cryptocurrency, and
provide us with initial understanding of social networks rooted
in and driven by anti-social constraints.
Index Terms—Social networks, Bitcoin, Cryptocurrency
I. INT RO DU CTI ON
Bitcoin is a complex socio-cyber-physical system, e.g., [1],
consisting of a decentralized peer-to-peer payment network, a
currency unit, publicly preserved transaction history kept in
a massively-replicated public ledger, i.e., the blockchain, an
algorithm that controls money generation, and an ownership
verification mechanism using public-key cryptography, where
each Bitcoin address consists of a pair of public and private
keys [2]. The process of creating new coins in the system
is called mining. The mining process is computationally
expensive. Any node connected to the Bitcoin network can
participate in Bitcoin mining either as a part of a group of
miners (called mining pool) or individually. In pooled mining,
the generated coins are shared based on each member’s
contributed computational power.
I. Alqassem is with the Department of Computer Science, Purdue Univer-
sity, West Lafayette, IN 47907, USA, Email: ialqasse@purdue.edu.
I. Rahwan is with the MIT Media Lab, Massachusetts Institute of Technol-
ogy, Cambridge, MA 02139, USA, Email: irahwan@mit.edu.
D. Svetinovic is with the Center on Cyber-Physical Systems, Department
of Computer Science, Khalifa University of Science and Technology, Abu
Dhabi, UAE, Email: davor.svetinovic@ku.ac.ae (*Corresponding Author).
Many commentators liken Bitcoin’s present state to the
early days of the Internet, and suggest that its technology will
transcend financial transactions to encompass all kinds of new
social transactions.
The structure and evolution dynamics of various social
networks are well-studied [3], [4], [5], [6], [7], [8]. How-
ever, the Bitcoin transaction graph represents a novel kind
of network that consists of global financial transactions car-
ried out by users hidden behind pseudonyms represented by
public keys (accounts, addresses, or public keys are used
interchangeably to refer to users’ unique identifiers used in
Bitcoin system). These transactions are continually validated
by Bitcoin computational nodes; running on users’ computers
and other specialized mining hardware, added to blocks, and
newly generated blocks appended to the blockchain, which
serves as a key innovation of the Bitcoin network [2].
One of the main driving forces behind the creation of
Bitcoin was to counter the systematic move towards more
transparency (i.e., reduction of privacy) and centralization.
The original cash-based financial system got replaced with
credit cards, audited transactions, automatic reporting to gov-
ernmental entities, etc. As a reaction to such increased lack
of privacy, centralization of control, and extensive monitoring,
there appeared a need to develop a system that re-establishes
and protects the financial privacy. The second driving force
behind the creation of Bitcoin was to develop a currency with
a predictable, algorithm-controlled inflation rate, as opposed
to the unpredictable, human-controlled inflation rate of fiat
currencies.
As such, Bitcoin presents a paradox of social and anti-social
forces. On one hand, Bitcoin’s main function is to facilitate
economic transactions among individuals, which is a highly
social function. Indeed, by eliminating expensive, trustworthy
intermediaries, Bitcoin reduces the cost of transactions, thus
facilitating more open economic transactions, transcending
geographical and social boundaries.
On the other hand, at the core of the Bitcoin design
philosophy are strong anti-social elements. Among Bitcoin’s
user community, there is a strong emphasis on privacy and
anonymity, manifested in the fact that transactions only require
cryptographic public keys in order to take place. Furthermore,
the Bitcoin system embodies greater trust in algorithmic,
rather than human, control of the money supply. In addition,
Bitcoin’s key distinguishing feature is its ability to process
and verify transactions without transaction intermediaries that
hold privileged positions in the network. As such, Bitcoin is
distrustful, and arguably subversive, of centralized financial
institutions or intermediaries that may abuse their power.
2
These seemingly contradictory social and anti-social ele-
ments of Bitcoin are, in fact, the key features behind its dis-
ruptive proliferation. However, we still lack a deep quantitative
understanding of Bitcoin’s adoption, use and growth dynamics.
In order to acquire such understanding, we need to quantify
the way in which Bitcoin’s transaction network evolves over
time, and to characterize the structural properties produced by
the social and anti-social forces and their interactions. This
will pave the way towards more complex analyses and may
facilitate the development of scalable algorithms and online
services that provide real-time insights into the blockchain and
its vulnerabilities.
In this paper, we inspect the Bitcoin transaction network’s
evolution dynamics. Our findings indicate that despite the
distinction in the nature of Bitcoin’s transaction network when
compared to other social networks, the Bitcoin transaction
network follows the common normal evolution patterns, i.e.,
the densification power law and shrinking diameter (although
the diameter shrinks only after the network reaches maturity).
On the other hand, we find that the absolute value of the
transaction graph diameter is extremely large when compared
to the other social networks which can be attributed to the
presence of long chains of transactions. The transaction graph
has less dense communities. Furthermore, the majority of
public keys (>90% of total public keys in the network)
represent transitional or intermediate accounts with incom-
ing and outgoing edges but zero cumulative balances. Most
of the intermediate accounts are generated to complicate
tracing users’ wealth and identities. These observations can
be attributed to the anti-social component of the behavior
among Bitcoin users, i.e., they generate and discard accounts
constantly to preserve and even further protect their anonymity.
II. RELATED WORK
We cover three categories of related work. First, we discuss
the related work that examined the blockchain data either
as a single snapshot or at different time frames for vari-
ous purposes, such as analyzing the level of privacy and
anonymity in Bitcoin. Second, we discuss the related work
which examined the universal characteristics that govern graph
growth over time, from which we borrowed the graph growth
metrics. Third, we discuss the related work that covers various
applications of social network data analytics studies.
A. Blockchain Data Studies
Kondor et al. [9] investigated the evolution of basic charac-
teristics of the blockchain over time. They identified two main
phases of Bitcoin’s life, the initial phase and the trading phase.
The initial phase lasted until fall 2010, during which there was
no real-world value associated with a bitcoin. Then MtGox,
the previously popular Bitcoin exchange, went online and the
Bitcoin trading phase has begun, through which bitcoins have
gained market value. They examined the degree distribution,
degree correlation and clustering coefficients, and wealth
distribution. They showed that preferential attachment was
shaping both the degree of Bitcoin addresses and the wealth
distributions among these addresses which are fundamentally
related in Bitcoin transaction network. In our analysis, we
examine various network characteristics that were not covered
here. We also repeat our analysis on the approximation of
Bitcoin user graph based on a heuristic, that we discuss later,
and was built based on the fact that all input addresses of a
transaction must belong to a single entity that holds the private
keys of these addresses.
Ron et al. [10] examined different statistical properties of
Bitcoin transaction graph and analyzed the graph of the largest
transaction that took place at the time of their analysis, May
13th 2012, where an entity sent 90,000 bitcoins to itself
multiple times. Instead of looking at global network properties
over time such as market price of bitcoins, number of daily
transactions, etc. they examined the typical behavior of Bitcoin
users e.g., the balances kept in their accounts, addresses associ-
ated with the largest balances, the size distribution of Bitcoin
transactions, and the percentage of micropayments. One of
their interesting findings was that the majority of bitcoins were
not circulating in the network. Other findings were: (i) Bitcoin
users tended to move their bitcoins large number of times in
self-loops manner between different accounts, (ii) large sums
of bitcoins were distributed in a binary tree-like structure,
(iii) Approximately 156,722 addresses were associated with
Mt.Gox exchange at the time of their study. Their dataset
contained transaction data up to block 180,000 (3,120,948
addresses). This research did not look into the evolution of the
transaction graph over time, instead they focused on statistical
properties in a single snapshot.
Maesa et al. [11] presented a scalable clustering algorithm
that constructed Bitcoin user graph with less false positives,
thus they reduced the size of the original transaction graph.
Then they analyzed the time evolution of the generated user
graph with a late starting point (January 2013), after the
Bitcoin system has matured and gained significant financial
impact. They examined the nodes richness in terms of their
degree and accumulated balances, and they confirmed the
previous finding [9] that the Bitcoin network is a scale-free
one where the richness is concentrated, and where high-degree
nodes play a vital role for network connectivity and their
constructed graph confirmed small-word phenomenon. They
also showed that the distribution of clusters follow a power-
law model. They inferred some address identities relying on
publically available tag datasets. In our analysis, we look into
different network characteristics in the full Bitcoin transaction
graph before and after the system gained its popularity and
we highlight how the users behavior changes over time to
adapt to the system. We do not examine the in- and out-degree
distributions and the distribution of the wealth in the network
since that were already verified in previous research.
In the next three papers, [12], [13], [14], the authors ana-
lyzed the transaction graph in order to investigate the claimed
anonymity that Bitcoin promised to offer. In doing so, they
matched some Bitcoin addresses to real-world entities while
constructing the Bitcoin transaction graph. Our work, however,
inspects different network characteristics without touching the
anonymity subject. We think Bitcoin supports pseudonymity
not full anonymity and the users of the network are responsible
to manage their addresses, i.e., public keys, in order to protect
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their privacy.
Fleder et al. [12] analyzed seven-month blockchain data
between March 25th 2013 and October 25th 2013 for the
purpose of examining the anonymity levels in Bitcoin. They
developed a system to link public keys to their real-world
entities by web scraping Bitcoin forum, public social network,
donation sites, and other services where Bitcoin fans publicly
announced their addresses. They also applied the PageRank
algorithm to figure out the most important nodes, i.e., the ones
that received large traffic like SatoshiDICE1). Furthermore,
they de-anonymized a number of Bitcoin users, e.g., they
identified some of Bitcoin forum users: (i) who gambled at
SatoshiDICE, (ii) who were one hop away from Silk Road,2
(iii) who had direct transactions with Wikileaks. In addition to
an address belonged to FBI. This work focused on the level of
anonymity that Bitcoin was supposed to offer and showed that
it is possible to link real-world identities to Bitcoin addresses.
Meiklejohn et al. [13] explored the evolution of Bitcoin
network through tracing the flows of both unspent and in-
circulation bitcoins over time. Their methodology was divided
into two stages. First, they identified public keys of well-
known Bitcoin merchants and services (such as Mt. Gox and
Silk Road) by making direct purchases from them. Addi-
tionally, they extracted self-labeled public keys from Bitcoin
forum. Then, they clustered the users of known public keys
into a graph where the nodes represent known services instead
of merely representing anonymous addresses. They, by no
means, aimed to de-anonymize all Bitcoin network, but rather
they leveraged certain characteristics of Bitcoin protocol (e.g.,
multi-input transactions in which all input addresses belong to
the same entity, and Bitcoin change) to reveal the identities
of certain Bitcoin services, then categorized these services
in order to calculate their overall balances, the percentage
of transactions they involved in, etc. Their dataset contained
blockchain data up to block 231,207 (16,086,073 transactions
and 12,056,684 addresses).
Reid et al. [14] explored the limits of anonymity in Bitcoin
transaction and user networks. They showed that one could
easily figure out the total balance and incoming and outgoing
transaction of Bitcoin public keys and users. As an example
they visualized all WikiLeaks’ payments and degree distri-
bution over time and the number of transactions involving
its public key. As a case study of potential risks to the
anonymity in Bitcoin, they investigated the 25,000 bitcoins
theft reported in June a3th , 2011, and they developed a tool to
trace the stolen bitcoins which was transferred among several
public keys. Their results showed that it is easy for Bitcoin
centralized service providers (such as exchanges and wallet
services) that have details on users’ identities to identify and
track considerable portions of their users. Furthermore, They
suggested some enhancements to Bitcoin protocol to protect
user’s privacy. It is worth pointing out that this research is
1The biggest Bitcoin gambling website.
2An online marketplace uses bitcoins to trade in illegal drugs, firearms and
other goods, operated as a Tor hidden service. It was shut down temporarily
by FBI in October 2013 but it reopened again as Silk Road 2.0 in November
2013.
among the earliest attempts that analyzed Bitcoin network.
Their dataset contained 1,253,054 public keys.
B. Social Network Analysis
Leskovec et al. [15] examined graph time evolution pro-
cess in terms of the average node in- and out-degree and
the effective diameter in nine graphs obtained from four
diverse datasets. These datasets are: (i) ArXiv citation graph
(29,555 papers, 352,807 edges), (ii) U.S. patent citation graph
(3,923,922 patents, 16,522,438 citations), (iii) autonomous
systems graph, this one exhibits addition and deletion of
nodes and edges from November 1997 to January 2000, (iv)
bipartite affiliation graphs (57,381 nodes, 133,170 edges).
These datasets were divided into regularly spaced snapshots in
time. And the results they obtained showed that densification
power laws3and shrinking diameters4are fundamental natural
phenomena in all the graphs they examined. To produce graphs
that capture shrinking diameter, heavy-tailed in- and out-
degree distributions, and densification properties they proposed
the Forest Fire Model. Indeed, shrinking diameter is rather
surprising; as one would expect the graph’s diameter to grow
as the number of nodes increases. Shrinking diameter may be
attributed to two reasons. One reason is the addition of edges,
as in the stylized Erd ¨os-Renyi random graph model where
the diameter of the largest connected component (LCC) starts
quite large and then it decreases as edges are being added
continually. An alternative reason is what happens in real
graphs where the nodes become well-connected to each other
over time even after a graph reaches maturity, i.e., the diameter
continues to decrease in a steady manner when the LCC
contains almost all nodes. From this research we borrowed
the characteristics which define how real graphs evolve over
time. We also compare and contrast the growth patterns of
Bitcoin to the growth patterns observed in this research while
highlighting the novelty of Bitcoin network.
C. Applications
Kong et al. [16] have emphasized the need for social
network and media analysis within the context of the systems
development. They have explored the evolution patterns of
popularity with respect to the burst forms and decays. They
found that predicting the trends of popularity evolution is
beneficial for decision making for various types of systems,
e.g., emergency management, business intelligence, and pub-
lic security. They evaluated their approach using tweets in
SinaWeibo, a Chinese Twitter-like social media platform, with
positive results and improvements.
Liu et al. [17] have demonstrated the importance of the
social network analysis with respect to preserving system
properties such as privacy and anonymity. They emphasized
that the network analysis is even more effective when multiple
network analysis are performed for the identification of the
users. This is putting the context of our focus on the financial
social network in the perspective with respect to the other types
3Number of edges grows super-linearly in the number of nodes.
4Diameter decreases as network grows.
4
of social networks. While their method has shown positive
results, it is unclear how it would perform within the context
of blockchain-based social networks.
Zhang et al. [18] have studied evolutionary game dynamics
of multiagent systems on multiple community networks. Given
the fast evolution of blockchain systems and their potential in-
tegration with the artificial intelligence (AI) systems is opening
even further application areas of the social network analysis
in the context of blockchain systems. The further integration
of the various blockchain systems is expending the analysis
opportunities on multiple social network systems. The ability
of agents to perform this analysis and interpret the data, will
open up a whole another range of application opportunities
for blockchain in complex AI-backed social networks.
Chang et al. [19] have used blockchain network data to
analyze different patterns of transactions occurring in the
Bitcoin network in order to cluster addresses that share the
same ownership. This clustering approach has increased our
ability to trace Bitcoin ownership thus potentially reducing the
privacy of the users.
III. MET HO D A ND RE S ULT S
The temporal information of Bitcoin transactions embedded
in the blockchain enables us to inspect the evolution dynamics
and the key structural properties of this innovative payment
network, where Bitcoin accounts represent the nodes and the
transactions occurring between these accounts correspond to
the edges. We identify 11 time-spaced sequential snapshots of
the blockchain between January 2009 and September 2014.
Six-month interval separates any two consecutive snapshots,
except for the last one which contains the blockchain trans-
actions up to the last block in our dataset. Table I shows our
snapshots statistics.
TABLE I
MAI N CH AR ACTE RI STIC S OF B LOC KC HAIN SNA PS HOTS .
Snapshot
index
Block depth #nodes #edges End date
1 18,650 1,054 1,098 03-Jul-09
2 32,800 2,877 3,630 03-Jan-10
3 64,000 24,404 34,965 03-Jul-10
4 100,800 126,353 259,669 03-Jan-11
5 134,500 1,060,648 2,962,425 03-Jul-11
6 160,400 2,736,480 8,554,243 03-Jan-12
7 187,300 4,662,573 20,875,170 03-Jul-12
8 215,000 8,725,003 50,567,140 03-Jan-13
9 244,600 14,998,319 102,040,630 03-Jul-13
10 278,400 24,882,840 165,402,563 03-Jan-14
11 319,359 46,043,947 398,145,539 06-Sep-14
In Bitcoin there is a special type of transaction without input
addresses, these transactions are called coinbase transactions.
One coinbase transaction is generated per block to send block’s
mining reward and transaction fees (whenever available) to
miners who participated in creating that block. The input
address of all coinbase transactions are mapped to a dummy
source address, then all coinbase transactions are excluded
from the subsequent analysis. Including coinbase transactions
would distort the results as they do not represent actual
transactions occurring between Bitcoin users or services but
merely transactions that generate coins in the system.
Two distinct stages of Bitcoin evolution are identified, i.e.,
the initial stage and the trading stage [9]. The initial stage
continued until the first half of 2010. After that, Bitcoin started
to attract growing number of users and online service providers
such as Mt. Gox exchange which went online in July 2010 and
Slush’s pool; the first mining pool that started in December
2010. Then, Bitcoin was recognized as a cryptocurrency and
a payment system, thus it gained a real purchase value and
its trading stage has begun after the beginning of 2011. While
the period in between represents a transitional stage. During
which, Bitcoin was adapted by more than amateur beginners
but it was still not yet recognized as a payment system neither
as a cryptocurrency. Fig. 1 shows how this intermediate stage
acts as a tipping point in the history of the first decentralized
cryptocurrency. Here we quantify the evolution of Bitcoin
and we show that some network properties differ noticeably
throughout these stages.
A. Bitcoin Accounts
There is no upper bound on the number of accounts a
Bitcoin user may have, nor a limit exists on the number
of transactions’ neighbours, unlike many of social networks
which constrain the maximum allowable number of outgo-
ing/incoming links. Moreover, in Bitcoin it is considered a
good practice to generate different key pairs to receive the
various incoming transactions in an attempt to maintain users’
anonymity by complicating the tracking of addresses’ owners
and their wealth. This results in the emerging of different
nodes types (i.e., Bitcoin account categories) which we cat-
egorize based on incoming transaction, outgoing transaction,
and total balance each account accumulates. These categories
are:
•Checking accounts: appeared as source and destination
of one or more transaction and have cumulative balance
greater than zero.
•Saving accounts: appeared only as destination of trans-
action(s) with cumulative balance greater than zero.
•Intermediate (transitional) accounts: accounts with zero
cumulative balance. These accounts are mostly created by
Bitcoin user or service, e.g., mixing or exchange service,
to transfer money between other accounts. A fraction of
these accounts may belong to users departing the network
and selling all their coins.
As Fig. 1 depicts, during the initial stage, saving accounts
were dominant since bitcoins did not have corresponding
purchase value in fiat money and consequently no merchants
were accepting them in exchange for goods or services. At
that stage, the checking and intermediate accounts represented
accounts owned by the early adopters who were trying or
testing the Bitcoin system. Later on, during the latter stage,
the intermediate accounts formed more than 90% of the total
created accounts. This reveals an expected common behavior
among Bitcoin users, i.e., they generate and discard public
keys constantly to preserve their anonymity which results in a
continually increasing transaction volume in the network. On
5
the other hand, the percentage of saving accounts has relatively
diminished in the trading stage compared with the initial stage.
While the absolute number of newly created checking accounts
went up by several orders of magnitude, from less than 30 in
July 2009 to more than 250K in September 2014. This can be
an indication of more people nowadays considering Bitcoin as
a viable medium of exchange.
Two points can emphasize the aforementioned indication.
First, the growing merchant adoption and the increasing num-
ber of service providers supporting Bitcoin payment directly
or indirectly, (i.e., via conversion services such as Coinbase
and BitPay) have enhanced Bitcoin’s utility. Currently, big
businesses and multinational corporations such as Microsoft,
Dell, and Expedia support Bitcoin payments, moreover users
can buy a wide range of physical goods with bitcoins, different
gift card businesses accept bitcoins, and numerous physical
stores, hotels, restaurants, and charities are welcoming Bitcoin
payments [20]. Second, even though saving accounts have not
faded away, Bitcoin currently can not be viewed as a stable
store of value due to its high volatile price. Roughly speaking,
the average market price around the beginning of July 2013
reached 85 USD, six months later this value jumped to 793
USD, while in March 2015 it was about 270 USD. This
high price fluctuation leaves the user uncertain whether the
bitcoins he has today will worth the same value tomorrow,
hence incentivizes him to invest them in daily transactions
(checking or speculation in Bitcoin) rather than saving them.
Unlike the early adopters who used to keep their coins for the
hope of making more profit for the exact opposite reasons:
(i) due to limited options they had for spending their bitcoins
on, and (ii) the chances were high at that time for bitcoin’s
purchase value to increase day after day.
B. Largest Connected Component (LCC) and its Diameter
The LCC of a graph connects the majority of the graph
nodes. We examine the connectivity of Bitcoin transaction
graph over time by quantifying the percentage of Bitcoin
accounts taking part of its LCC, in addition to the diameter
of this LCC as shown in Fig. 1. In graph theory, the diam-
eter represents an important topological metric that helps in
understanding the size and density of a network. To find the
diameter of a graph (or its LCC), first we find the shortest
paths between each pair of vertices. Then, the path with the
maximum length represents the diameter of the graph, hence
the diameter is the largest shortest path.
Bitcoin addresses are almost fully connected with more than
99.9% of Bitcoin accounts taking part of the LCC by the
end date of the taken last snapshot. Network connectivity, in
the context of the nodes taking part of the LCC, in Bitcoin
scenario is similar to was reported for the LCCs of other social
networks. For example, in May 2011, the LCC of Facebook
had 99.91% of the total registered users [21]. In August 2009,
the LCC of Twitter had 94.8% of twitter profiles [22]. Further,
similar high percentage of nodes connecting to the LCC of
their graphs was observed for arXiv and U.S. patent citation
graphs [4].
There is a significant difference between the absolute value
of the transaction graph’s diameter in the last taken snapshot
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Checking
Intermediate
Saving
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B
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0.00
0.75
0.50
1.00
Relative size
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LCC relative size
LCC diameter
5000
4000
3000
2000
1000
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Diameter
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Fig. 1. (A) The evolution of Bitcoin account categories. A growth trend
towards intermediate accounts after the beginning of trading stage (vertical
dashed line). Intermediate accounts have incoming and outgoing transactions
but zero cumulative balances. Bitcoin users generate and discard such accounts
as a general practice to maintain their anonymity and avoid financial tracking.
(B) The evolution of the relative size of the transaction graph’s LCC and
its diameter. More than 99.9% of Bitcoin accounts are taking part of the
LCC as of September 2014. Similar high percentages are reported for nodes
connecting to the LCC in other social networks such as Twitter, Facebook, and
arXiv citation graph. After the beginning of the trading stage (vertical dashed
line), Bitcoin starts attracting growing number of users, therefore the graph’s
diameter expands, its transaction graph becomes sparser and the distances
between nodes increase continually until mid-2012. The expansion in diameter
at the beginning is observed for the earliest Facebook and Google+ datasets.
Later on, the diameter starts decreasing monotonically. The Shrinking diameter
after the network reaches maturity is also one of the observed phenomenon in
social networks, i.e., the diameter continues to decrease even after the LCC
contains almost all nodes since the graph becomes denser. The absolute values
of transaction graph’s diameter are two-orders-of-magnitude larger than what
is reported for social networks such as Facebook and Twitter which can be
attributed to the presence of long chains of transactions.
(>2000) and the reported diameter values in a single snapshot
of other social social networks. For example the diameter of
Facebook is 41, the diameter of Twitter is 18, and the diameter
of Google+ is 22 as reported in [23]. Four possible causes of
this dramatic increase in the diameter of the transaction graph:
•Anonymity which acts as an incentive for Bitcoin sup-
porters to create several accounts to transfer their unspent
coins.
•Thieves usually exhaust the network by generating enor-
mous number of public keys to transfer and spread the
stolen bitcoins. For instance, in [14] it was reported that
more than 34,100 new addresses were created by the
suspicious of Bitcoin theft which occurred in June 2011.
•The change addresses generated by Bitcoin client to
transfer the remainder of the payment back to the payer,
as bitcoins cannot be spent partially (Fig. 2).
•Bitcoin mixing services such as Bitcoin Fog and BitLaun-
dry which offer mixing users’ bitcoins with each other
by generating many new accounts. Mixing services are
generally used for Bitcoin laundry to complicate trailing
illegal fund [24].
All of the aforementioned points lead to the presence of
long transaction chains which in turn increases the shortest
6
paths between graph nodes.
A1 A2
A1
A2
C1
Scenario 1
Scenario 2
A1
A2
C1
A3
C2
A1 A2
A3
Scenario 3
Scenario 4
Fig. 2. In Bitcoin the change is not returned to the same address to
protect user’s privacy. Here, we assume that blue circles represent addresses
owned by the same user. In scenarios 1&2, the user who owns address A1
sends a transaction to the user who owns address A2. The second scenario
demonstrates how the change address concept protects user’s privacy because
it is difficult to distinguish the recipient(s) of the payment. In scenarios 3&4,
the user who owns address A1sends another transaction from the change
of previous transaction (partial amount of that change). In scenario 3, there
is no change address so the bitcoins are sent from the same address A1.
In scenario 4, the bitcoins are transferred from the change address C1to
an address A3owned by another user, a new change address C2is created
after this transaction. In this example we try to demonstrate how these change
addresses increase the distance between nodes (here A2and A3).
C. Densification Power Law
103105
Number of nodes
107
1010
108
106
104
102
Number of edges
Edges
0.2 x 1.1952
*
July ’09
Sep ’14
Fig. 3. The transaction graph follows densification power law, i.e., the average
degree increases over time. The densification exponent is 1.1952.
The densification power law, or growth power law is an
empirical observation examined by other researchers when
studying the evolution of real graphs over time [4]. This law
of graph evolution states that the growth of graph’s edges is
super linear in terms of the growth of its nodes. The Bitcoin
transaction graph obeys this power law. In Bitcoin evolution
context, it indicates despite that Bitcoin addresses (i.e., public
and private key pairs) are being created continually, the edges
grow super linearly as a function of the growth of newly
added accounts. In other words, the growth of the network is
attributed to the increase number of transactions, which means
increase adaption and use of the Bitcoin financial system over
time.
The densification power law is represented mathematically,
as follows:
E(t)∝N(t)αwhere 1< α ≤2
E(t)and N(t)are the number of graph’s edges and nodes
respectively at each timestamp t. The Bitcoin transaction graph
is becoming denser and its densification fits a power-law
pattern with a slope α= 1.1952, as shown in Fig. 3. The
values of the densification exponents are 1.69 and 1.12 for
arXive and Email networks, respectively. Although Bitcoin
users change their accounts frequently, i.e., new nodes are
being added continually to the transaction graph, still the
growth of the transaction graph’s edges is superlinear as a
function of the growth of its nodes over time, similar to what
was reported for other social networks such as IMDB actors
to movies network and Email network [4].
D. Degree Assortativity
The degree assortativity acts an ingredient of community
structure in a graph [25]. Degree assortativity coefficient mea-
sures whether or not graph’s nodes have tendency to interact
with similar nodes with regard to their in and out degree in
directed graph (or degree in undirected one) [26], [27]. Its
value lies between [−1,1], where values close to or equal to 1
is a sign of assortative mixing. 0indicates neutral assortativity.
Negative values reveal the opposite, i.e., “disassortativity”.
Social groups of real world typically have assortative mixing
as ‘birds of a feather flock together”. Whereas there is no rule
for online social networks [28]. For example, Flickr shows
assortative mixing (0.202), while Youtube demonstrates the
opposite (−0.033).
To measure degree assortativity in the transaction graph
self-edges are excluded as they are irrespective to how nodes
connect to each other. Table II shows negative assortativity
over time. Since in Bitcoin payment system, transactions occur
at two different levels: (i) internal, i.e., between different
accounts that belong to the same user, and (ii) external,
i.e., between different users in the network. In the internal
transactions users usually transfer their coins from high-
degree checking accounts to low-degree saving accounts. In
the external transactions bitcoins are usually sent from low-
degree addresses to high-degree addresses owned by known
merchants and service providers.
E. Time-evolving Community Structure
Communities are graph modules with internally dense
edges but relatively sparse external connections. We examine
the evolution of statistical properties of transaction graph’s
communities, i.e., hub dominance, scaled link density, and
7
TABLE II
DEG RE E A SSO RTATIV IT Y CO EFFI CI ENT,TH ES E VAL UE S AR E
STATI STIC ALLY SI GNIFI CA NT (T-TES T P -VALU E ¡0.05).
Date Degree assortativity
coefficient
03-Jul-09 -0.239
03-Jan-10 -0.043
03-Jul-10 -0.021
03-Jan-11 -0.034
03-Jul-11 -0.022
03-Jan-12 -0.041
03-Jul-12 -0.04
03-Jan-13 -0.041
03-Jul-13 -0.041
03-Jan-14 -0.027
06-Sep-14 -0.011
community size distribution which are proposed in [29]. Self-
edges cannot be indicative of how communities evolve thus
we discard them to simplify our graph, similar approach is
followed in [30].
Modularity is the first thing to look at when examining
community structure. It is a quality index for measuring the
presence of community structure in a graph by comparing the
edge coverage of a community with the coverage an algorithm
would achieve in a randomized null-model graph [31].
Modularity value depends on the community detection
algorithm used, in addition to how modular a network is. Its
value lies between [−0.5,1.0], where higher values indicate
more modular networks, as such transaction graph tends to
be a modular network (Fig. 4). Remarkably, the number of
communities does not grow all the time, e.g., the number of
the total evolving communities declined in six-month period
between January 2011 and July 2011 which indicates that
smaller communities getting merged into larger ones. This
merge in communities coincided with the operation of the
first Bitcoin pooled mining service “Slush’s pool” which
attracted an increasing number of miners as soon as it was
released. The growth of evolving communities, on the other
hand, can be attributed to split in existing communities or/and
new nodes joining the network and establishing new well-
connected clusters.
ە
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1.0
0.8
0.6
0.4
0.2
0.0
Modularity
ەە
ە
ەە
ە
ە
ە
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2000
1500
1000
500
0
2500
Number of communities
ە
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Modularity
Number of communities
Fig. 4. Network’s modularity and the number of evolving communities.
We use a parallel implementation of Louvain method to detect Bitcoin
communities. Based on these relatively high modularity values, the transaction
graph tends to have modular structure.
1) Scaled link density: This property is defined as the
average internal degree5of nodes within a community.
ρ=2t
s(s−1) Link density
˜ρ=ρs =2t
s−1Scaled link density
Where, tis the number of edges within a community and s
represents the size of that community, i.e., the number of nodes
forming it. Scaled link density reveals community’s nature.
For example, tree-like community has number of edges equals
to the lower limit (ttree =s−1), substituting this value
in the second equation above gives us 2, therefore tree-like
communities always have scaled link density value equals to
2. Whereas in a full clique, each node is connected to all other
nodes, i.e., the number of edges in the undirected clique equals
to the upper limit (tclique =s(s−1)
2), substituting this value in
the scaled link density equation gives us a value of s, therefore
clique-like communities always have scaled link equals to s.
To examine the dependency of this property on the size
of the community, the median of scaled link densities are
plotted as a function of communities’ sizes over time as
illustrated in Fig. 5. The median values are chosen here
given the skewness in the distribution of scaled link density
values. Bitcoin communities’ scaled link densities lie in the
interval [2,5], closer to the lower limit, which indicate tree-like
structure behind the majority of Bitcoin communities (Fig. 5).
Whereas social networks have denser communities than trees
but sparser than cliques based on the finding of a previous
study [29].
2) Hub-dominance: How dominant are the biggest hubs
within Bitcoin communities? This can be quantified according
to the following formula:
Hub −dominance =max(kin)
s−1
Where, max(kin)is the maximum degree of a node within
a community. The maximum possible degree is s−1when
a central node within a community is connected to all other
nodes in its community, consequently the value of the above
ratio will equal to 1 in such extreme case. For the majority
of social networks this ratio decline with community size
until dominant hubs almost vanished from large communities.
However, in the Email and the web graphs the dominant hubs
existed independent of community size [29]. We also study
this property as a function of community size over time. In the
transaction graph there is a hybrid existence of dominant and
non-dominant hubs. Roughly speaking, smaller communities
(s≤100) tend to have full- to half-dominant hubs opposite to
larger ones (s > 104) which lack dominant nodes as depicted
in Fig. 6.
3) Distribution of communities’ sizes: The distribution of
communities sizes is an important statistic describing com-
munity structure. After the beginning of the trading stage the
community size distribution almost preserve the same shape.
We run a comparative test that leverages the log likelihood
ratios to compare the fit between various pairs of distributions
and find that the exponentially truncated power law represents
the best fit.
5Internal degree: node’s degree in the subgraph of the community.
8
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ەە
ەە ە ە ە
Median scaled link
density
10
2
20
30
40
ە ە ەە
ەە
ەەە
ەەە
ە
ە
ە
ە
s <= 100
100 < s <= 10,000
s > 10,000
AB
C
Fig. 5. Scaled link density. (A) Tree-like subgraph with scaled link density
equals to 2. (B) Clique-like subgraph with scaled link density equals to the
number of nodes 5. (C) The evolution of median values of scaled link density
in transaction graph as a function of community size s. In spite of community
size, the scaled link density median values are close to the lower limit which
indicates a tree-like structure behind the majority of Bitcoin communities,
which indicates “split or merge” of coins between accounts. The median value
of scaled link density spikes at the end for large communities >104. More
investigation is needed to figure out the nature or causes of these relatively
sparse communities.
F. Inequality as measured by Gini Index
Here we study the distribution of wealth among these
accounts. From economics perspective, Lorenz curve measures
the inequality of the wealth distribution. In Fig. 7 the diagonal
(45◦) represents the line of perfect equality. The increase in
the area between this diagonal and Lorenz curve indicates the
greater the gap in wealth distribution among Bitcoin accounts
over time. Gini coefficient can be computed from this curve,
Kondor et al. conducted a detailed analysis into the Bitcoin
wealth distribution [9].
IV. DIS CUS SI ON
Bitcoin aims at establishing a global financial network fa-
cilitating transactions among people from all around the world
without the need for expensive, trustworthy intermediaries.
Despite the different purposes of the various social networks
and Bitcoin transaction network, one can observe universal
dynamics such as the densification power law, shrinking
diameter, and modular structure as discussed previously in
the results section, and the power-law degree distribution as
reported in the previous work [9].
Social networks generally exhibit addition and deletion of
nodes and edges over time. However, in Bitcoin, after a trans-
action gets confirmed, all of the addresses encapsulated within
that transaction can never be deleted from the blockchain.
This criterion together with the financial nature of Bitcoin
network stimulate an anonymity-seeking behaviour among
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1.0
0.8
0.6
0.4
0.2
0.0
0HGLDQKXEíGRPLQDQFH
ە
ە
ە
ە
ە
ە
ە
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ە
ە
ە
ە
ە
ە
ەەە
s > 10,000
ە ە
ە
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s <= 100
100 < s <= 10,000
A B
C
Fig. 6. Hub-dominance. (A) In this subgraph, the yellow node has the
maximum degree, it is connected to 4 out of 5 nodes, therefore the hub-
dominance value equals to 0.8. (B) The circular subgraph lacks of hub
presence. (C) Shows the evolution of median values of hub-dominance
as a function of community size s. The presence of hubs within Bitcoin
communities depends directly on community size, i.e., the hub-dominance
values decline with community size until dominant hubs vanish from large
communities. Similar to what is reported for other social networks. Noticeably,
communities of size >104appeared only after January 2011, after the Bitcoin
gained real market value and consequently started to attract growing number
of users and services. We examine different values of community size (s) and
the same trend holds for all values.
Bitcoin users which in turn leads to the key distinction between
Bitcoin transaction network and other social networks.
Thus, the vulnerable anonymity together and the inability to
erase addresses or transactions from the blockchain threaten
users with potential financial tracking. This is especially the
case if a user converts from a fiat currency to bitcoins from a
traditional financial account. In this scenario, their real identity
is linked to their Bitcoin account [14]. To prevent this identity
linking, the users engage in even further anonymity seeking
behavior. This is done using the features of the Bitcoin’s
core design which is equipped with the necessary capabilities
emphasizing anonymity and privacy, i.e., the concept of change
addresses in addition to user’s ability to generate as many new
addresses as desired.
Further, to improve anonymity, mixing services, which are
called sometimes laundry services, have been developed by
Bitcoin supporters. These services, when implemented prop-
erly, hide any connection between the user’s source address
(the account used to deposit an amount of bitcoins into the
service) and the destination address (the account used to with-
draw bitcoins) [24]. Consequently, Bitcoin users, sometimes
with the aid of mixing services, create various categories of
accounts as discussed previously and minimize the reusability
9
0.0 0.2 0.4 0.6 0.8 1.0
0.8
0.6
0.4
0.2
0.0
1.0 2009
2010
2011
2012
2013
2014
Cumulative share of Bitcoin accounts
from lowest balance to highest
Cumulative share of total bitcoins
Fig. 7. The evolution of Lorenz curve. The x axis is the cumulative share of
Bitcoin accounts from lowest balance to highest. The y axis is the cumulative
share of total bitcoins. The increase in the area between this diagonal and
Lorenz curve indicates the greater the gap in wealth distribution among
Bitcoin accounts. The distribution of wealth in the Bitcoin financial system
has become heterogeneous since 2011, i.e., users who own less than 10% of
addresses almost control the whole wealth. Prior to 2011, the Bitcoin network
was in its trial version where a few enthusiasts and developers (the number
of users by the end of initial stage was less than <8,000) tried the system
and split their coins among many accounts.
of their addresses by splitting or merging their coins in long
transaction chains which result in a huge diameter, different
account categories, and sparse tree-like communities which
distinguish the Bitcoin anti-social network from the other
social networks.
We also examined the same graph properties for an approx-
imation of Bitcoin user graph. In that approximation graph,
a single node represents a group of addresses that belong to
the same user 6. To generate an approximation of Bitcoin user
graph we used a heuristic that was developed and effectively
used in the previous research [10], [13]. This heuristic relies
upon the fact that all input addresses of a transaction must
belong to a single entity that holds the private keys of
these addresses. Quoting Satoshi Nakamoto from the original
Bitcoin white paper [2]: “Some linking is still unavoidable
with multi-input transactions, which necessarily reveal that
their inputs were owned by the same owner.” Establishing
a user graph from a transaction graph can be viewed as a
variation of the Union-Find known graph algorithm [32] as
illustrated in Fig. 9. However, the exact users of Bitcoin
cannot be determined precisely because the Bitcoin protocol
was intentionally designed to maximize user’s anonymity by
minimizing the possibility of linking the different addresses
owned by the same user.
The analysis of the approximation user graph confirmed
our previous findings since we discovered similar properties
in the approximation user graph: same large diameter, con-
6A user can have multiple nodes representing them in that graph, hence
this is just an approximation.
firmation of the densification power law, the disassortative
mixing, in addition to high modularity values (within the
range (0.70,0.92)) which, as stated earlier, reflect the presence
of a community structure. We even found close similarities
between the underlying trends of scaled link density and hub-
dominance median values as shown in Fig. 8. These results
strengthen our reasoning behind the unique nature of the
Bitcoin.
● ● ● ●
●●
● ●
●
●
0.0
0.2
0.4
0.6
0.8
1.0
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KXEíGRPLQDQFH
í
í
í
í
2011
í
2012
í
2012
í
í
í
2014
í
●
●
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●●
●●
●
●●●●●●●
● ● ● ● ● ● ● ● ●●
0HGLDQVFDOHGOLQN
density
2
10
20
40
●●
●
●●●●●●
●●●●●●●
●
●
●
s <= 100
100 < s <= 10,000
s > 10,000
$
%
C
Fig. 8. (A) Similarly, the scaled link density median values for the ap-
proximation graph indicates a tree-like structure behind the majority of the
approximation user graph communities. The spike shown previously in Fig.
5 vanishes indicating those relatively denser communities where mapped to
a single entity in the approximation graph. (B) Here as well, our finding
indicates that the presence of hubs in our approximation graph depends
directly on community size.
From the systems perspective, it was observed that some of
these anti-social incentives are effecting ritical system prop-
erties such as security and privacy, e.g., [33], [34], [35]. The
anti-social incentives are leading to formation or disintegration
of certain network communities. This in turn is leading to the
improper use or the intentional misuse of the overall system.
These community alteration present serious threats to a subset
of the system properties that we identified: decentralization,
longevity (of the system that’s supposed to evolve over next
hundreds of years), trust, participation incentive, privacy, se-
curity, and usage ethics. As such, our contribution in under-
standing and measuring social network properties that lead to
the identification of the anti-social incentives and properties
represent a contribution with a potentially significant systems
impact in the design of this new generation of cryptocurrency
networks.
Given the recent expansion of the blockchain use as a
system infrastructure to support other kinds of mission critical
systems, such as smart grids, Internet of Things (IoT), au-
tonomous driving vehicles, health records management, assets
trading, etc., e.g., [34], [36], [37], [38], we are shifting from
Bitcoin as a socio-cyber network [1] to full blockchain-based
socio-cyber-physical systems. This integration is putting a
10
Transaction ID Sending Address ID Receiving Address ID
Approx. User
ID
1 A H 1
1 D 1
2 C L ?
2 F M ?
2 H ?
3 D C 1
3 G 1
4 E M 1
4 G 1
Fig. 9. The addresses {A, D }are inputs to the same transaction, on this
account they are owned by the same entity. Address {D}appeared as sending
address in transactions {1,3}then all sending addresses of both transactions
belong to the same user. Moreover, address {G}appears as a common input
address to the transactions {3,4}, which leads us to conclude that a single
entity holds the private keys of {A, D, G, E }and that entity initiated all
the three transaction {1,3,4}. We cannot assign a new user id to the input
addresses of the second transaction until we see the complete list of all
transactions; we might encounter a common address that link them to the
aforementioned user.
combination of additional system properties of safety and trust
as critical with respect to potential anti-social incentives in
these new mission critical systems. To deal with these issues,
we have to develop additional social network measures and
to work on design of community detection technologies. This
will help us support the development of blockchain-enabled
trust infrastructures that can ensure sufficient levels of privacy,
security, safety, trust and overall dependability. This must be
done in the context of planning for systems longevity, i.e.,
these systems are supposed to last hundreds of years, e.g,
Bitcoin’s longevity is critical to assume if it is to be considered
as the financial system infrastructure for these mission critical
socio-cyber-physical systems.
Finally, while this paper covers data from 2009–2014 that
correspond to the initial phase and trading phase identified
in [9], the paper does not cover the period from late 2014
until present that represents the currently ongoing heavy mass
media and heavy financial speculation phase. While this can
be considered as a limitation of this work, we believe that the
data from the ongoing speculation phase is worth studying in
its own light once the speculation phase is over. At the time
of the writing, we were unable to take into account either the
mass media coverage variable or heavy financial speculation
variable neither qualitatively nor quantitatively.
V. CO NCL US ION
In summary, Bitcoin represents a move from relatively
local, transparent social networks created through the use of
traditional fiat currencies to relatively global, semi-anonymous
social networks created through the use of cryptocurrencies,
with Bitcoin being the leading example. If we assume that the
ultimate goal of social networks is to connect globally, one
could argue that the traditional currency networks could be
considered anti-social. The need to control a fiat currency and
to have a certain level of transparency within a local currency
network creates control conflicts among the sovereigns. This
in turn prevents effective, inexpensive expansion of the local
social financial networks evident through expensive financial
conversion protocols and services.
To fight this anti-social component of the local traditional
currency social networks, Bitcoin relies upon a set of its
own anti-social forces as observed in this paper. As we
have seen in our results, the evolutionary dynamics of the
Bitcoin as the most popular cryptocurrency provides us with
the initial understanding of social networks rooted in and
driven by anti-social behaviours. We can conclude that it is
indeed the optimal balance of the social and anti-social forces
that is critical for the success and acceptance of a particular
currency and the corresponding financial social network. And
the enforcement of anti-social behaviours is critical for the
users, even at the expense of adding the additional social
network noise as the results have shown.
As a part of our future research, we will work on the de-
velopment of other cryptocurrency network specific measures
and community detection approaches, and combine them with
our natural language analysis approach [39], [40] and generic
infrastructure models [41] to provide enhanced privacy, secu-
rity, and trust blockchain solution in the smart grid systems
domain. This will be combined with the use of questionable
arbitrary data recorded in the blockchains [34] in order to
tackle the issues of higher-level system usage ethics and trust-
ethical constraints.
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Israa Alqassem is a PhD student at Purdue uni-
versity, USA. She is interested in machine learning,
blockchain technology, and the IoT. Currently, she
is a visiting research student at Ludwig Maximilian
University of Munich, Germany. Her research focus
is the development of statistical methods and com-
putational tools for analyzing genomic data.
Iyad Rahwan is the AT&T Career Development
Professor and an Associate Professor of Media Arts
& Sciences at the MIT Media Lab, where he leads
the Scalable Cooperation group. A native of Aleppo,
Syria, Rahwan holds a PhD from the University of
Melbourne, Australia. He is an affiliate faculty at the
MIT Institute of Data, Systems and Society (IDSS),
and member of the MIT Taskforce on the Work of
the Future.
Rahwan’s work lies at the intersection of computer
science and human behavior, with a focus on collec-
tive intelligence, large-scale cooperation, and the societal impact of Artificial
Intelligence and social media. His early work explored how social media can
be used to achieve unprecedented feats, such as searching an entire continent
within 9 hours, and re-assembling shredded documents. He led the winning
team in the US State Department’s Tag Challenge, using social media to locate
individuals in remote cities within 12 hours using only their mug shots.
Recently, Rahwan led a team that crowdsourced 40 million decisions from
people worldwide about the ethics of autonomous vehicles. Through a series
of projects, he also exposed tens of millions of people world-wide to new
implications of AI, such as bias in machine learning, human-AI creativity
and the ability of AI to induce fear and empathy in humans at scale.
Another theme that interests Iyad is the future of work and human-
machine cooperation. He demonstrated the world’s first human-level strategic
cooperation by an AI, and innovated new methods to anticipate the potential
impact of AI on human labor.
Iyad Rahwan’s work appeared in major academic journals, including
Science and PNAS, and features regularly in major media outlets, including
the New York Times, The Economist, and the Wall Street Journal.
12
Davor Svetinovic is an Associate Professor of Com-
puter Science at Masdar Institute, Khalifa University
of Science and Technology, UAE. He received his
PhD (2006) degree in Computer Science from Uni-
versity of Waterloo, Canada. Previously, he worked
as a visiting professor and research affiliate at the
Massachusetts Institute of Technology (MIT); and
as a postdoctoral researcher at Lero – the Irish
Software Engineering Center, Ireland, and Vienna
University of Technology, Austria. He leads the
Strategic Requirements and Systems Security Group
(SRSSG), and he has extensive experience working on complex multi-
disciplinary research projects. He has published over 65 papers in leading
journals and conferences. His current research interests include systems secu-
rity and privacy, blockchain engineering, cryptocurrencies, and requirements
engineering. He is a Senior Member of IEEE and ACM.
