Google matrix of the world trade network Leonardo Ermann CNEA - - PowerPoint PPT Presentation

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Google matrix of the world trade network Leonardo Ermann CNEA - - PowerPoint PPT Presentation

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Google matrix of the world trade network Leonardo Ermann CNEA (Buenos Aires, Argentina) Colab. Dima Shepelyansky July 24th 2012, Spectral properties of complex networks ECT, Trento supported by EC FET Open project NADINE Outline

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SLIDE 1

Google matrix of the world trade network

Leonardo Ermann CNEA (Buenos Aires, Argentina)

July 24th 2012, “Spectral properties of complex networks” ECT, Trento

supported by EC FET Open project NADINE

  • Colab. Dima Shepelyansky
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SLIDE 2

Outline

“Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • Google Matrix of WTN
  • 2D-rank of WTN
  • WTN models

2

  • Multi-Product Network
  • Crisis model
  • Ecological Ranking

(nestedness) I II III

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I Google Matrix of the WTN

3 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 4

Google Matrix of the WTN

United Nation Commodities Trade Network

all countries of UN, from 1962 to 2011, all commodities or some specific products

Money Matrix

Mi,j = U$S(j → i)

4 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • L. Ermann and D.L. Shepelyansky, APPA,
  • Vol. 120, A-158 (2011), arXiv:1103.5027, http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank
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SLIDE 5

Google Matrix of the WTN

United Nation Commodities Trade Network

all countries of UN, from 1962 to 2011, all commodities or some specific products

Money Matrix

Mi,j = U$S(j → i)

G G

ExportRank ImportRank CheiRank PageRank *

M PageRank, CheiRank ImportRank, ExportRank

( ˜ K, ˜ K∗) (K, K∗)

GP = P G∗P ∗ = P ∗

4 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • L. Ermann and D.L. Shepelyansky, APPA,
  • Vol. 120, A-158 (2011), arXiv:1103.5027, http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank
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SLIDE 6

G and G* matrices of the WTN (2008)

M G G*

a l l c

  • m

m

  • d

i t i e s

5 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 7

G and G* matrices of the WTN (2008)

M G G*

a l l c

  • m

m

  • d

i t i e s c r u d e p e t r

  • l

e u m

5 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 8

PageRank, CheiRank and Spectrum

PageRank, CheiRank, ImportRank, ExportRank

α = 0.85 α = 0.5

Zipf law P~1/K

all commodities crude petroleum

6 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 9

PageRank, CheiRank and Spectrum

PageRank, CheiRank, ImportRank, ExportRank

Spectra α = 1

α = 0.85 α = 0.5

Zipf law P~1/K

all commodities crude petroleum

6 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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2d ranking “all commodities”

7 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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PageRank, CheiRank vs. ImportRank, ExportRank

8 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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PageRank, CheiRank vs. ImportRank, ExportRank

countries are treated on equal democratic ground G-20 ~ 74%

˜ K∗ = 11 − → K∗ = 16 ˜ K∗ = 13 − → K∗ > 20 ˜ K∗ = 15 − → K∗ = 11 ˜ K∗ = 19 − → K∗ = 12

8 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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2d ranking: crude petroleum

its trade network in this product is better and broader than the one of Saudi Arabia (1st)

Russia ˜ K∗ = 2 → K∗ = 1 Iran ˜ K∗ = 5 → K∗ = 14 Kazakhstan ˜ K∗ = 12 → K∗ = 2

its trade network is restricted to a small number of nearby countries. is practically the only country which sells crude petroleum to the CheiRank leader in this product Russia.

9 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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2d ranking: barley and cars

Ukraine (K* 1st to 6th) USA (K* 8th to 3rd) France (K* 7th to 3rd) Thailand (K* 19th to 10th) 10 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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WTN model

  • Gravity model of trade:

(symmetric)

  • Random model

(preserves Zipf law)

Mi,j = gmimj/Di,j Mi,j = ✏i✏j/ij ✏i,j ∈ [0, 1)

t:: all commodities (1962, 2008); b: crude petroleum (2008), random model

11 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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2d ranking evolution

12 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Model statistics

13 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Model statistics

13 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Time evolution and velocity K and K* from1962 to 2009

∆v2 = [K(t) − K(t − 1)]2 + [K∗(t) − K∗(t − 1)]2

average per K + K∗

average in [K + K∗ − 10, K + K∗ + 10]

Velocity square vs. K+K*

14 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Velocity evolution

K + K∗ ∈ [1, 40] K + K∗ ∈ [41, 80] K + K∗ ∈ [81, 120] K + K∗ ∈ [1, 20] K + K∗ ∈ [21, 40] K + K∗ ∈ [41, 60]

200 400 600 1960 1970 1980 1990 2000 201

years

0.1 1 10 100

v

2

15 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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K and K* ranking evolution (some examples)

Japan France

  • Fed. Rep. of Germany and Germany

Great Britain (sublimation?) USA Argentina India China (deposition) USSR and Russian Fed.

16 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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II Ecological Ranking (nestedness)

17 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Nestedness

18 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 1937 Hulten 1957 Darlington 1975 Daubenmire

biogeography

bipartite networks: species - sites (islands, plants, etc) Causes: rates of extinction and colonialization (ay least 7 mechanisms)

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SLIDE 24

Nestedness

18 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 1937 Hulten 1957 Darlington 1975 Daubenmire

biogeography

bipartite networks: species - sites (islands, plants, etc) Causes: rates of extinction and colonialization (ay least 7 mechanisms)

quantifying nestedness

BINMATNEST

M.A. Rodriguez-Girones and L. Santamaria, Journal of Biogeography 33, 924 (2006)

isocline

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Mutualistic Networks (countries-products)

M (i)

p,c = Nc

X

c0=1

M p

c,c0

M (e)

p,c = Nc

X

c0=1

M p

c0,c

m(i,e) = M (i,e)/Mmax

1968 2008

19 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • L. Ermann and D.L. Shepelyansky, arXiv:1201.3584
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SLIDE 26

Binary mutualistic Networks

Q(i,e)

c,p

= ( 1 if m(i,e)

c,p

≥ µ if m(i,e)

c,p

< µ

20 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 27

Binary mutualistic Networks

Q(i,e)

c,p

= ( 1 if m(i,e)

c,p

≥ µ if m(i,e)

c,p

< µ

fraction of 1s imports exports

20 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 28

EcoloRank Countries

Exports Imports money ranking

21 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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EoloRank products

imports exports

22 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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EoloRank products

imports exports money rank

22 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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III Multi-products and Crisis

(work in progress)

23 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Multi-product WTN

(multiplexity in networks) NC=227 (2008)

(SITC1 Rev.)

Np=10 (1d) Np=61 (2d) Np=182 (3d)

S C

24 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 33

Multi-product WTN

(multiplexity in networks) NC=227 (2008)

(SITC1 Rev.)

Np=10 (1d) Np=61 (2d) Np=182 (3d)

S C

24 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Multi-product WTN

K-K*

(tracing out products)

1d 2d 3d

25 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 35

Multi-product WTN

K-K*

(tracing out products)

1d 2d 3d 1d 2d 2-dimensional PageRank

25 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Crisis

weight balance

2008; w>0.05 (~20%) w>0.035 26 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 37

Crisis

weight balance

2008; w>0.05 (~20%) w>0.035 26 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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Crisis model

toy model:

(1) if bi ≥휅 ⇒ imports of i are closed (2) compute G,G* ⇒ bi ⇒(1) Cc (local) Nc (global) t 훕 휅 fp

27 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 39

Crisis model

toy model:

(1) if bi ≥휅 ⇒ imports of i are closed (2) compute G,G* ⇒ bi ⇒(1) Cc (local) Nc (global) t 훕 휅 fp

27 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 40

Crisis model

toy model:

(1) if bi ≥휅 ⇒ imports of i are closed (2) compute G,G* ⇒ bi ⇒(1) Cc (local) Nc (global) t 훕 휅 fp

27 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 41

Crisis model

toy model:

(1) if bi ≥휅 ⇒ imports of i are closed (2) compute G,G* ⇒ bi ⇒(1) Cc (local) Nc (global) t 훕 휅 fp

27 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

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SLIDE 42

Conclusions

28 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • PageRank-CheiRank of WTN

(network properties, democratic, i-e symmetry)

  • Comparison with Import-Export
  • Model of M (directed by randomness, preserves Zipf law)

I

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SLIDE 43

Conclusions

28 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • PageRank-CheiRank of WTN

(network properties, democratic, i-e symmetry)

  • Comparison with Import-Export
  • Model of M (directed by randomness, preserves Zipf law)

I

  • Analogy with ecology (nestedness) for EcoloRank

(countries and products, topology of bipartite binary network) II

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SLIDE 44

Conclusions

28 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • PageRank-CheiRank of WTN

(network properties, democratic, i-e symmetry)

  • Comparison with Import-Export
  • Model of M (directed by randomness, preserves Zipf law)

I

  • Analogy with ecology (nestedness) for EcoloRank

(countries and products, topology of bipartite binary network) II

  • Multi-Product Network (general approach)

(2-dimensional PageRank, β parameter controls internal market)

  • Crisis(analyze b and b(t+1)-b(t), toy model to study global crisis)

III

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SLIDE 45

Conclusions

28 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento

  • PageRank-CheiRank of WTN

(network properties, democratic, i-e symmetry)

  • Comparison with Import-Export
  • Model of M (directed by randomness, preserves Zipf law)

I

  • Analogy with ecology (nestedness) for EcoloRank

(countries and products, topology of bipartite binary network) II

  • Multi-Product Network (general approach)

(2-dimensional PageRank, β parameter controls internal market)

  • Crisis(analyze b and b(t+1)-b(t), toy model to study global crisis)

III Thank You