Bitcoin Network. Transaction & User Network. Power Law distribution

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