Rich gets richer-Bitcoin Network
-
Upload
abdullah-khan-zehady -
Category
Education
-
view
45 -
download
3
Transcript of Rich gets richer-Bitcoin Network
![Page 1: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/1.jpg)
Rich Gets Richer !
Even In Bitcoin
Network?
Announcement of Current Research State..
Zehady Abdullah Khan
Lab of Professor Hidetoshi Shimodaira
Bachelor 4th year,
Mathematical Science Course,
Department of Information and Computer Sciences,
School Of Engineering Science,
Osaka University.
3/30/2015
![Page 2: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/2.jpg)
Bitcoin Transaction
3/30/2015
![Page 3: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/3.jpg)
Bitcoin Transaction Data
#Vertices : 13,086,528
#Directed Edges: 44,032,115
Transaction Data from January 2010 ~ May 2013
3/30/2015
![Page 4: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/4.jpg)
Unit Transaction & Network
Edges
Input AddressOutput Address
ID 1
ID 2
….
ID n_I
ID 1
ID 2
….
ID n_O 3/30/2015
4
# Possible Edge = n_I * n_O per tx
• Edges are not unique for simplicity
![Page 5: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/5.jpg)
Growth of Bitcoin Network
3/30/2015
245 USD/BTC
Novermber 5, 2013
* What were the prime
Factors for
Price Increase ?
Bitcoin Exchange Started
2 Phases: 1. Initial Phase 2. Trading Phase
![Page 6: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/6.jpg)
Yearly In Degree
Distribution
3/30/2015
α= 2.18
Power Law Dist: pin(kin) ∼ kin-2.18
![Page 7: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/7.jpg)
Yearly Out Degree
Distribution
3/30/2015
Power Law Dist: pout(kout) ∼ kout-2.06
α= 2.06
![Page 8: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/8.jpg)
Wealth Inequality : Gini Coefficient
3/30/2015
0 £G £1
G =0 Perfect equality
1 Complete Inequality
ì
íï
îï
For a population uniform on the values
of di
![Page 9: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/9.jpg)
G in Bitcoin
3/30/2015
Initially Phase: G for in degree is high Users mostly stored bitcoins
Trading Phase: Gin almost converged with Gout
![Page 10: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/10.jpg)
Pearson & Clustering
Coefficient
3/30/2015
![Page 11: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/11.jpg)
Degree Distribution
3/30/2015
Degree = Indegree +
Outdegree
• Number of Lower degree
(0~1000)
nodes are very high.
• Lots of isolated nodes.
• Few hubs
![Page 12: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/12.jpg)
Bitcoin Balance Statistics
3/30/2015
1 BTC = 383USD
(Nov 12,
2013)
Min 1st Q Median 3rd Q Max
BTC 0.00 0.00 0 0.00 111,100
USD 0 0 0 0 42,560,000
Total # of nodes Nodes with Non-
Zero Balance
Nodes with
Zero Balance
13,085,528 1,621,222 (12 %) 11464306 (88%)
Total # of BTC Total Generated BTC Left
21,000,000 11,942,900 9057100
![Page 13: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/13.jpg)
BTC balance Chart
3/30/2015
All Nodes Non-zero balance Nodes
![Page 14: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/14.jpg)
Rich Nodes
3/30/2015
Rich balance Nodes
> 10000 USD
Total Rich Nodes 67,512
(0.515%)
Unique Rich
Nodes
66,386
(0.507% )
Total Nodes 13,086,528
Unique Nodes 6,994,357
(53%)
Total Balance
(USD)
4,259,869,852
Rich Node
Balances
(USD)
3,960,047,047
(93%)
![Page 15: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/15.jpg)
3/30/2015
Degree Centrality: Eigenvector Centrality
3/30/2015
Which are the most important or central vertices in the network ?
xi : the centrality of the node i
Aij : the adjacency matrixi
j
Aij = 1
xi' = Aijx j
j
å
x ' = AxRepeat….
x(t) = Atx(0) : centrality vector after t steps
x(0) = civi ; vi is the eigenvector of xii
å
x(t) = At civi = cilitvi =
i
å l1
t cilil1
æ
èç
ö
ø÷
t
vi ---> c1l1
tv1 (t-->¥) i
åi
å
Ax = l1x
xi = l1
-1 Aijx jj
å
![Page 16: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/16.jpg)
Different Network
Measures
3/30/2015
![Page 17: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/17.jpg)
Eigenvector Centrality in Bitcoin
Network
3/30/2015
Largest Eigen Value, l1 = 761.6418
ID 3247203 3247205 3247200 3247206 3247202 3247197
Centralit
y 1 0.083688264 0.054296171 0.050453962 0.047525502 0.032626146
ID 3247199 3247191 3247196 3247209 3247193 3247215
Centralit
y0.0244427
27 0.020694083 0.017641267 0.017346914 0.015898656 0.014387567
ID 3247213 3247190 3247195 3247194 3247180 3247192
Centralit
y0.0138252
13 0.013527306 0.012857685 0.01278417 0.011125401 0.010684955
…………………………. Total 13041891 centralities.
![Page 18: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/18.jpg)
Degree Centrality: Katz Centrality
3/30/2015
xi = a Aijx j + bj
å
; a, b are positive constants
Here a keeps the balance.
x = aAx + b1 ; 1=(1,1,1,...)
a -> 0 , x =b1
x = (I-aA)-11
(I-aA)-1 diverges when
| A-a -1I | = 0 => a -1 = l1
Therefore, a <1
l1
Node A has eigen vector centrality 0
Unexpectedly Node B has eigen vector
centrality 0
![Page 19: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/19.jpg)
Page Rank
3/30/2015
xi =a Aijx j
k jout
+ bj
å 1
For any j , if k jout = 0 , then put k j
out =1
In Matrix Term,
x = aAD-1x + b1
x = (I -aAD-1)-11= D(D-aA)-11
a < l, where l is the largest eigenvalue of AD-1
For undirected graph,
l = 1 with eigenvector v = (k1,k2,k3,....)
If a vertex with high Katz centrality points to a large number of other vertices, all
those vertices will gain high centrality !!!!
i
All other nodes gains high
centrality if the node i
has high Katz centrality
![Page 20: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/20.jpg)
Betweenness Centrality
3/30/2015
Measures the extent to which a vertex
lies on paths between other vertices.
nist =1 if vertex i lies between the shortest path from s to t
0 else
ìíï
îï
üýï
þï
xi = nist; st
å
xi = nist s¹t
å
xi =nist
gst ; gst = number of shortest paths from s to t
s¹t
å
![Page 21: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/21.jpg)
Closeness Centrality
3/30/2015
Measures the mean distance from a vertex to other vertices.
Mean shortest path from i,
li =1
ndij
j
å ; dij : length of the shortest path from i to j
li =1
n-1dij
j¹i
å
Closeness centrality Ci
Ci =1
li
Redefining,
Ci =1
n-1
1
dijj¹i
å
Mean shortest path of the network
l =1
n2dij =
ij
å1
nli
i
å
![Page 22: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/22.jpg)
References1. Do the rich get richer? An empirical analysis of the BitCoin transaction
network. MIT tech
Daniel Kondor,∗ Marton Posfai, Istvan Csabai, and Gabor Vattay ,Department of Physics of Complex Systems,Eotvos Lorand University, Hungary
2. Networks An Introduction
M.E.J Newman
3. Albert, R. and Barabasi, A.-L. (2002). Statistical mechanics of complex networks. Reviews of modern physics 74 (1), 47
4. Quantitative Analysis of the Full Bitcoin Transaction Graph. http://eprint.iacr.org/2012/584
Ron, D. and Shamir, A. (2012).
5. http://bitcoin.org/about.html
6. http://www.vo.elte.hu/bitcoin
3/30/2015
![Page 23: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/23.jpg)
The End
3/30/2015
![Page 24: Rich gets richer-Bitcoin Network](https://reader033.fdocuments.in/reader033/viewer/2022051414/55aa7ab01a28ab076d8b45aa/html5/thumbnails/24.jpg)
What’s Next ?
Detail Dynamics of transaction
Non-parametric estimation of preferential
attachment function.
Network Visualization of important Bitcoin entity
Extracting Interesting Bitcoin Phenomenon
Bitcoin price prediction.
3/30/2015