Multiproduct world trade network Leonardo Ermann CNEA (Buenos - PowerPoint PPT Presentation

Multiproduct world trade network Leonardo Ermann CNEA (Buenos Aires, Argentina) Colab. Dima Shepelyansky Klaus Frahm Alexei Chepelianskii Networks and data mining July 1st, 2015 School for advanced sciences of Luchon

Motivations Google approach to the World Trade Network L. ERMANN Multiprod WTN July 1st 2015, Luchon

Outline 1) G and G* introduction 2) WTN 3) multiproduct WTN 4) EcoloRank given by nestedness L. ERMANN Multiprod WTN July 1st 2015, Luchon

Google Matrix thanks to Klaus introduction of G matrix • directed networks centrality measure: • easy to compute Brin and Page (1998) • Spectral Indices incoming links • non-local properties directed network adjacency matrix L. ERMANN Multiprod WTN July 1st 2015, Luchon

Google Matrix thanks to Klaus introduction of G matrix • directed networks centrality measure: • easy to compute Brin and Page (1998) • Spectral Indices incoming links • non-local properties weighted adjacency matrix and dangling nodes directed network L. ERMANN Multiprod WTN July 1st 2015, Luchon

Google Matrix thanks to Klaus introduction of G matrix • directed networks centrality measure: • easy to compute Brin and Page (1998) • Spectral Indices incoming links • non-local properties PageRank directed network Google Matrix L. ERMANN Multiprod WTN July 1st 2015, Luchon

Google Matrix 2D rankings L.E, Chepelianskii and Shepelyansky, Jour. Phys. A 45, 275101 (2012). PageRank-CheiRank 2d ranking wiki: K-K* plane K- Chepelianskii (2010) O. Zhirov and Shepelyansky,(2010), LE, Chepeliansskii, Shepelyansky JPA(2012)

World Trade Network Import-Export trade database: United Nation Commodities Trade Network http://comtrade.un.org/db/ * Each year from 1962 to 2011 (2014) * All UN countries: ~ 220 (Nc=227 in 2008) * Product classification (SITC Rev. 1): Np=61 * Trade volume is given in USD (N=13847 x 50 years) Money Matrices c,c 0 = $ ( c 0 → c ) M c,c 0 = $ ( c 0 → c ) M p L. ERMANN Multiprod WTN July 1st 2015, Luchon

Google matrix of the WTN G PageRank GP = P M * G CheiRank G ∗ P ∗ = P ∗ ExportRank ImportRank ( ˜ K, ˜ ( K, K ∗ ) K ∗ ) ImportRank, ExportRank PageRank, CheiRank Democracy in countries but not in products L. ERMANN Multiprod WTN July 1st 2015, Luchon

all commodities and given products (N=227) M G G* all commodities Spectra PageRank, CheiRank, ImportRank, ExportRank α = 0 . 5 α = 1 Zipf law P~1/K less symmetric all comm petroleum L. ERMANN Multiprod WTN July 1st 2015, Luchon

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 ˜

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

2d rank evolution L. ERMANN Multiprod WTN July 1st 2015, Luchon

2d rank evolution 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]

2d rank evolution Japan France Fed. Rep. of Germany and Germany Great Britain (sublimation?) USA Argentina India China (deposition) USSR and Russian Fed. L. ERMANN Multiprod WTN July 1st 2015, Luchon

Google of multi-product WTN 2) WTN (multiprod) 1) WTN (all com. or 1 prod) N=13847 N=227 prop to Vp of each c personalized vector non-interacting products reduced Pp for all c 2nd iteration L. Ermann and D.L. Shepelyansky, APPA, Vol. 120, A-158 (2011), http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank L. Ermann and D.L. Shepelyansky, EPJB (2015).

2d ranking of countries (multiproducts) L. ERMANN Multiprod WTN July 1st 2015, Luchon

2d reduced ranks P-C I-E L. ERMANN Multiprod WTN July 1st 2015, Luchon

2d ranking of products 1963 1978 1993 2008 L. ERMANN Multiprod WTN July 1st 2015, Luchon

PageRank CheiRank correlator I-E P-C L. ERMANN Multiprod WTN July 1st 2015, Luchon

multi-prod WTN spectrum eigenstate communities L.E, K. Frahm and D.L. Shepelyansky, EPJB 86, 193 L. ERMANN Multiprod WTN July 1st 2015, Luchon

Sensitivity to price variation L. ERMANN Multiprod WTN July 1st 2015, Luchon

Country balance P-C I-E L. ERMANN Multiprod WTN July 1st 2015, Luchon

Sensitivity to price variation II L. ERMANN Multiprod WTN July 1st 2015, Luchon

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 L. ERMANN Multiprod WTN July 1st 2015, Luchon

Nestedness m ( i,e ) = M ( i,e ) /M max N c N c X M p M ( e ) M ( i ) X M p p,c = p,c = c 0 ,c c,c 0 c 0 =1 c 0 =1 2008 1968 L. ERMANN Multiprod WTN July 1st 2015, Luchon

Binary mutualistic networks ( if m ( i,e ) 1 ≥ µ Q ( i,e ) c,p = c,p if m ( i,e ) 0 < µ c,p L. ERMANN Multiprod WTN July 1st 2015, Luchon

Ecolorank of countries Imports Exports money ranking L. ERMANN Multiprod WTN July 1st 2015, Luchon

Ecolorank of products imports exports money rank L. ERMANN Multiprod WTN July 1st 2015, Luchon

Conclusions • Google matrix of the WTN (democratic in countries, global network properties): 
 1) one product of all comm. (Nc) 
 2) multiprod (Nc x Np) 
 2d-ranking, spectrum, communities in eigenstates, correlation between P-C, comparison with I-E, new tool for trade analysis • Asymmetry in products • Time evolution analysis • Sensitivity to price variation (weak coupling between products) would lead to prediction of crisis and time evolution • Nestedness and EcoloRank Messi beaucoup!

2d global ranks L. ERMANN Multiprod WTN July 1st 2015, Luchon

2d global ranks

2d global ranks

product names