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

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 • Google Matrix of WTN • 2D-rank of WTN I • WTN models • Ecological Ranking II (nestedness) • Multi-Product Network III • Crisis model “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 2

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

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 M i,j = U $ S ( j → i ) L. Ermann and D.L. Shepelyansky, APPA, Vol. 120, A-158 (2011), arXiv:1103.5027, http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 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 M i,j = U $ S ( j → i ) G PageRank GP = P M * G CheiRank G ∗ P ∗ = P ∗ ExportRank ImportRank ( ˜ K, ˜ ( K, K ∗ ) K ∗ ) ImportRank, ExportRank PageRank, CheiRank L. Ermann and D.L. Shepelyansky, APPA, Vol. 120, A-158 (2011), arXiv:1103.5027, http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 4

G and G* matrices of the WTN (2008) M G G* s e i t i d o m m o c l l a “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 5

G and G* matrices of the WTN (2008) M G G* s e i t i d o m m o c l l a m u e l o r t e p e d u r c “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 5

PageRank, CheiRank and Spectrum α = 0 . 85 PageRank, CheiRank, ImportRank, ExportRank α = 0 . 5 Zipf law P~1/K all commodities crude petroleum “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 6

PageRank, CheiRank and Spectrum Spectra α = 1 α = 0 . 85 PageRank, CheiRank, ImportRank, ExportRank α = 0 . 5 Zipf law P~1/K all commodities crude petroleum “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 6

2d ranking “all commodities” “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 7

PageRank, CheiRank vs. ImportRank, ExportRank “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 8

PageRank, CheiRank vs. ImportRank, ExportRank countries are treated on equal democratic ground G-20 ~ 74% K ∗ = 11 − → K ∗ = 16 ˜ → K ∗ > 20 K ∗ = 13 − ˜ K ∗ = 15 − → K ∗ = 11 ˜ K ∗ = 19 − → K ∗ = 12 ˜ “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 8

2d ranking: crude petroleum K ∗ = 2 → K ∗ = 1 ˜ its trade network in this product is better and broader than the one of Saudi Arabia (1st) Russia K ∗ = 5 → K ∗ = 14 ˜ its trade network is restricted to a small number of nearby countries. Iran K ∗ = 12 → K ∗ = 2 ˜ is practically the only country which sells crude petroleum to the CheiRank leader in this product Russia. Kazakhstan “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 9

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) “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 10

WTN model • Gravity model of trade: M i,j = gm i m j /D i,j (symmetric) • Random model M i,j = ✏ i ✏ j /ij ✏ i,j ∈ [0 , 1) (preserves Zipf law) t:: all commodities (1962, 2008); b: crude petroleum (2008), random model “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 11

2d ranking evolution “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 12

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

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

Time evolution and velocity K and K* from1962 to 2009 Velocity square vs. K+K* ∆ v 2 = [ K ( t ) − K ( t − 1)] 2 + [ K ∗ ( t ) − K ∗ ( t − 1)] 2 average per K + K ∗ average in [ K + K ∗ − 10 , K + K ∗ + 10] “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 14

Velocity evolution 600 K + K ∗ ∈ [1 , 40] 400 K + K ∗ ∈ [41 , 80] K + K ∗ ∈ [81 , 120] 200 2 � v 0 100 K + K ∗ ∈ [1 , 20] 10 K + K ∗ ∈ [21 , 40] K + K ∗ ∈ [41 , 60] 1 0.1 1960 1970 1980 1990 2000 201 years “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 15

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

II Ecological Ranking (nestedness) “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 17

Nestedness biogeography bipartite networks: species - sites (islands, plants, etc) 1937 Hulten 1957 Darlington 1975 Daubenmire Causes: rates of extinction and colonialization (ay least 7 mechanisms) “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 18

Nestedness biogeography bipartite networks: species - sites (islands, plants, etc) 1937 Hulten 1957 Darlington 1975 Daubenmire 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 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 18

Mutualistic Networks (countries-products) N c N c M p M p M ( i ) X M ( e ) X m ( i,e ) = M ( i,e ) /M max p,c = p,c = c,c 0 c 0 ,c c 0 =1 c 0 =1 2008 1968 L. Ermann and D.L. Shepelyansky, arXiv:1201.3584 “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 19

Binary mutualistic Networks ( if m ( i,e ) 1 ≥ µ Q ( i,e ) c,p = c,p if m ( i,e ) 0 < µ c,p “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 20

Binary mutualistic Networks ( if m ( i,e ) 1 ≥ µ Q ( i,e ) c,p = c,p if m ( i,e ) 0 < µ c,p fraction of 1s imports exports “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 20

EcoloRank Countries Imports Exports money ranking “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 21

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

EoloRank products imports exports money rank “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 22

III Multi-products and Crisis (work in progress) “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 23

Multi-product WTN (SITC1 Rev.) (multiplexity in networks) N p =10 (1d) N p = 61 (2d) N C = 227 (2008) N p = 182 (3d) S C “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 24

Multi-product WTN (SITC1 Rev.) (multiplexity in networks) N p =10 (1d) N p = 61 (2d) N C = 227 (2008) N p = 182 (3d) S C “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 24

Multi-product WTN 1d 2d 3d K-K* (tracing out products) “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 25

Multi-product WTN 1d 2d 3d K-K* (tracing out products) 1d 2d 2-dimensional PageRank “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 25

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

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

Crisis model t toy model: C c (local) 훕 (1) if b i ≥ 휅 ⇒ imports of i are closed N c (global) 휅 (2) compute G,G* ⇒ b i ⇒ (1) f p “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 27

Crisis model t toy model: C c (local) 훕 (1) if b i ≥ 휅 ⇒ imports of i are closed N c (global) 휅 (2) compute G,G* ⇒ b i ⇒ (1) f p “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 27

Crisis model t toy model: C c (local) 훕 (1) if b i ≥ 휅 ⇒ imports of i are closed N c (global) 휅 (2) compute G,G* ⇒ b i ⇒ (1) f p “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 27

Crisis model t toy model: C c (local) 훕 (1) if b i ≥ 휅 ⇒ imports of i are closed N c (global) 휅 (2) compute G,G* ⇒ b i ⇒ (1) f p “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 27

Conclusions • PageRank-CheiRank of WTN (network properties, democratic, i-e symmetry) I • Comparison with Import-Export • Model of M (directed by randomness, preserves Zipf law) “Google matrix of the WTN”, L. Ermann July 24th 2012, ECT Trento 28