This document provides an overview and statistical analysis of the Bitcoin payment network from 2009 to 2014. It summarizes previous research on Bitcoin and describes the collection of over 10GB of Bitcoin transaction data to create a graph database. Statistical analysis was performed including community detection algorithms to estimate user networks from transaction networks, and analysis of the degree distributions and preferential attachment of nodes. Key findings include the identification of power law distributions and evidence that wealthy nodes tend to receive more Bitcoins over time.

1. Bitcoin landscape:
A statistical analysis of
the evolution of a fast-pacing
decentralized payment network.
Zehady Abdullah Khan
B4 09B12702,
Shimodaira Lab.
Department of Information and Computer Sciences,
School Of Engineering Science,
Osaka University.
2014-02-17
1

2. Bitcoin- A New Phenomenon
A virtual currency &
a payment system like
Credit Card, Pasmo or Suica.
An open source software published in
2009
by an Anonymous Programmer named
Satoshi Nakamoto
(Suspicion)
Kyoto U Professor
Shinichi Mochizuki
2

3. USD / BTC
Bitcoin is bigger than some national economy
Current Market Cap
About 8 billion USD
時価総額 約８０億ドル
Exchange Rate
為替レート： １ビットコインが何ドルか
3

4. Past Research
• Satoshi Nakamoto (2008) Bitcoin main paper. [1]
• Reid & Harrigan (2011) An Analysis of Anonymity in the Bitcoin
System.[2]
• Sarah Meikeljohn (2013) User Detection Algorithms. [3]
• Daniel Kondor, Marton Posfai, Istvan Csabai, and Gabor
Vattay (2013) An Empirical Analysis of Bitcoin transaction
network. [4]
4

5. Research Overview
Part 1
Data Collection
&
Creation of
Bitcoin Graph Database
Using Bitcoin
Data ( > 10GB)
From
Jan 2009 ~ Jan 2014
Part 2
Statistical Analysis
New
Transaction Network
+
Community Detection
&
Network Visualization
User Network
5

6. Estimation of User Network
Estimated User Network
Transaction Network
A
A
A
1
2
A
5
A
3
8
A
9
A
3
A
6
2 BTC
A
7
Jan 1, 2013
A
U1
U1
Estimation
Algorithm
t1
t2
1.5
2
U2
U2
4
t4
1.5
UU4
4
t3 1
A12
U3 3
U
A14
t5
t4
55.6
3
A13
5
t4
A
U5
U5
9
A11
A10
Uk : k- th user
Ak : k- th address
Data
#Addresses:
25,401,565
#Transactions: 150,097,987
Small User
Network
User Network
#Users:
#Edges:
11,920,531
74,894,291
6

7. Visualizing Wikileaks Network
Partial Transaction Network
#Addresses:
25, 687
#Transaction:
37,944
Partial User Network
#Users:
1708
#Edge:
1719
Estimation of
User Network
IN tk
def
:= Bitcoins received by user Uk up to time t
def
OUTtk := Bitcoins sent by user Uk up to time t
Bk
t
def
:= Bitcoin balance of Uk after time t
=IN tk - OUTtk
Wikileaks Bitcoin Balance
Wikileaks
Wikileaks
BWikileaks = IN December - OUTDecember
December
= (7177 - 4139) BTC
= 3038 BTC
» 1.6 M USD

8. Degree Distribution follows Power Law
t
outd k
P( ind )
t
def
:= In Degree of user U up to time t
k
def
:= Out Degree of user U up to time t
k
ind
c.c.d. f
U4
=3
out 4
d December =
2
outd
α
Power Law Distribution
p.d. f
in 4
d December
P( outd )
ind k
p(x) µ x -a
P(x) =
ò
¥
x
p(x)dx
ind
outd
2009-2012
2.005
1.895
2009-2013
2013
2.003
1.895
1.904
2.830
8

9. Non-paremtric Estimation of PA Function
No prior assumption of
power law.
R Package SNEPA
α = 1.005
Ak µ k1.005
Nodes with High Degree
Nodes with High Probability of
getting new edges
Preferent Attachment(PA)
Function Ak
9

10. Few Rich Nodes Getting Richer
inAugust
P (BDecember )
1e 0
0.79
IN July µ inJuly
BDecember
INJuly
Bitcoin Balance after time t,
def
B := IN t - OUTt
t
IN t
int
def
:= Bitcoins received up to month t
def
Rich nodes tend to
receive more bitcoins.
:= Bitcoins received in month t only
def
OUTt := Bitcoins sent up to month t
10

11. Community Detection & Network Visualization
Case Study :
Accumulation of huge amount of
Bitcoin
by FBI
in October 2013.
FBI
11

12. References
1. Bitcoin: A Peer-to-Peer Electronic Cash System B.(2008)
 Satoshi Nakamoto
2.
An Analysis of Anonymity in the Bitcoin System. (2011)
 Fergal Reid and Martin Harrigan
3.
A Fistful of Bitcoins: Characterizing Payments Among Men with
No Names.(2013)

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
5.
http://bitcoin.org
12

13. End of
Presentation
13

14. Additional Slides
14

15. What is Bitcoin?
• “Bitcoin” – An alternative payment network.
• “bitcoin”- The currency of the “Bitcoin” network.
• Each user creates multiple addresses for
better privacy.
15

16. USD / BTC
How big is bitcoin?
Limited amount: 21 million
Current Market Cap(市場資本総額)
About 8 billion USD
Bigger than
other national currencies.
(Exp- Jamaica,Laos,Georgia)
Rare &
Valuable
Currency Symbol : BTC
BTC
Address :31uEbMgunupShBVTewXjtqbBv5M
ndwfXhb
Analogy
E-mail: some@gmail.com
16

17. How Bitcoin Network works?
tx 1
Transaction Pool
tx 3
tx 2
…
Public Ledger
(Public transaction Book)
Registration
2009
tx 1
tx n
Bitcoin Block
tx 1
…
Secret
Number
tx 3
Bitcoin Mining
tx 1
25 BTC
Reward
tx 3
374123
243234
944553
345654
2014
17

18. National currencies with low market cap
18

19. Bitcoin Network Data
• Transactions from Jan 03,2009 ~ Jan 01,2013
o # Bitcoin Blocks = 279,530
o # Transaction
= 30,717,483
o # Addresses
= 25,401,565
• 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