Bitcoin has become very popular and you will frequently see it in internet news and in various financial reports.
Here you can see a simple transaction network of 5 bitcoin users where different color represents different users. Bitcoin users use bitcoin addresses to send and receive bitcoin. Here each node is a bitcoin address. Ak means the k-th address of the bitcoin network. Each edge is a transaction which holds the information about the transaction time and the amount of transacted bitcoin. Transaction network tries to hide the user identity to maintain user privacy by allowing users to create multiple bitcoin addresses. The first part of my research was to create my own program to estimate bitcoin users and create the user network from the transaction network. The user estimation algorithms I have modified are suggested in two research papers, first by researcher Martin Harrigan(Graph Drawing research group, University of Limerick) and the second by researcher Sarah Meikeljohn from UC San Diego. While estimating the users, I have calculated the degree, balance and other network measures for users. If t represents time, I have defined dtk as the degree of of k-th user after time t. Degree means the number of edges connected to a node. Btk is the balance of k-th user after time t.
Bitcoin Network Analysis
A statistical analysis of
the evolution of a fast-pacing
decentralized payment network.
Zehady Abdullah Khan
Department of Information and Computer Sciences,
School Of Engineering Science,
Bitcoin- A New Phenomenon
A virtual currency &
a payment system like
Credit Card, Pasmo or Suica.
An open source software published in
by an Anonymous Programmer named
Kyoto U Professor
USD / BTC
Bitcoin is bigger than some national economy
Current Market Cap
About 8 billion USD
• Satoshi Nakamoto (2008) Bitcoin main paper. 
• Reid & Harrigan (2011) An Analysis of Anonymity in the Bitcoin
• Sarah Meikeljohn (2013) User Detection Algorithms. 
• Daniel Kondor, Marton Posfai, Istvan Csabai, and Gabor
Vattay (2013) An Empirical Analysis of Bitcoin transaction
Bitcoin Graph Database
Data ( > 10GB)
Jan 2009 ~ Jan 2014
Estimation of User Network
Estimated User Network
Jan 1, 2013
Uk : k- th user
Ak : k- th address
Visualizing Wikileaks Network
Partial Transaction Network
Partial User Network
:= Bitcoins received by user Uk up to time t
OUTtk := Bitcoins sent by user Uk up to time t
:= Bitcoin balance of Uk after time t
=IN tk - OUTtk
Wikileaks Bitcoin Balance
BWikileaks = IN December - OUTDecember
= (7177 - 4139) BTC
= 3038 BTC
» 1.6 M USD
Degree Distribution follows Power Law
P( ind )
:= In Degree of user U up to time t
:= Out Degree of user U up to time t
d December =
Power Law Distribution
P( outd )
p(x) µ x -a
Non-paremtric Estimation of PA Function
No prior assumption of
R Package SNEPA
α = 1.005
Ak µ k1.005
Nodes with High Degree
Nodes with High Probability of
getting new edges
Few Rich Nodes Getting Richer
P (BDecember )
IN July µ inJuly
Bitcoin Balance after time t,
B := IN t - OUTt
:= Bitcoins received up to month t
Rich nodes tend to
receive more bitcoins.
:= Bitcoins received in month t only
OUTt := Bitcoins sent up to month t
Community Detection & Network Visualization
Case Study :
Accumulation of huge amount of
in October 2013.
1. Bitcoin: A Peer-to-Peer Electronic Cash System B.(2008)
An Analysis of Anonymity in the Bitcoin System. (2011)
Fergal Reid and Martin Harrigan
A Fistful of Bitcoins: Characterizing Payments Among Men with
Sarah Meiklejohn Marjori Pomarole Grant Jordan, Kirill Levchenko Damon
McCoy† Geoffrey M. Voelker Stefan Savage
4. Do the rich get richer? An empirical analysis of the BitCoin
transaction network. (2013)
Daniel Kondor, Marton Posfai, Istvan Csabai, and Gabor Vattay
What is Bitcoin?
• “Bitcoin” – An alternative payment network.
• “bitcoin”- The currency of the “Bitcoin” network.
• Each user creates multiple addresses for
USD / BTC
How big is bitcoin?
Limited amount: 21 million
Current Market Cap(市場資本総額)
About 8 billion USD
other national currencies.
Currency Symbol : BTC
How Bitcoin Network works?
(Public transaction Book)
Bitcoin Network Data
• Transactions from Jan 03,2009 ~ Jan 01,2013
o # Bitcoin Blocks = 279,530
o # Transaction
o # Addresses
• Transaction Network
o # Vertices = # Addresses = 25,401,565
o # Edges = About 150,000,000
• User Network
o # Vertices = 11,920,531
o # Edges = 74,894,291
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