Commodities Trading Network in Europe: R + igraph +SNA + network

Load Adjacency Matrix of Trading Network in Europe

	AUT	BEL	BGR	CYP	CZE	DNK	EST	FIN	FRA	DEU	GRC	HUN	ISL	IRL	ITA	LVA	LTU	LUX	MLT	NLD	NOR	POL	PRT	ROU	SVK	SVN	ESP	SWE	CHE	GBR
AUT	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
BEL	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	1
BGR	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
CYP	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0
CZE	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
DNK	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0
EST	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
FIN	0	0	0	0	0	0	1	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	1
FRA	0	1	0	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	1	0	0	1
DEU	1	1	0	0	1	1	0	1	1	0	0	1	1	0	1	1	1	0	0	1	0	1	0	0	1	1	1	1	1	1
GRC	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
HUN	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
ISL	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
IRL	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
ITA	0	0	1	1	0	0	0	0	1	1	1	0	0	0	0	0	0	0	1	0	0	0	0	1	0	1	1	0	0	0
LVA	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
LTU	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
LUX	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
MLT	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
NLD	0	1	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
NOR	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	1
POL	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
PRT	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0
ROU	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
SVK	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
SVN	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
ESP	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0
SWE	0	0	0	0	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	1
CHE	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
GBR	0	1	0	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Note:
abcd_0.9

Rescaling the node position with Fruchterman-Reingold Algorithm

Clustered by Louvain Community Detection Algorithm(Blondel et al. 2008) : groups = 4 and modularity score =0.36

EU_commodity_trading_network

## IGRAPH clustering multi level, groups: 4, mod: 0.36
## + groups:
##   $`1`
##   [1] "CYP" "GRC" "ITA" "MLT" "PRT" "ROU" "SVN" "ESP"
##   
##   $`2`
##   [1] "BEL" "BGR" "FRA" "LUX" "NLD"
##   
##   $`3`
##   [1] "AUT" "CZE" "DEU" "HUN" "ISL" "LTU" "POL" "SVK"
##   
##   $`4`
##   + ... omitted several groups/vertices

louvain_community_detection

## Community sizes
## 1 2 3 4 
## 8 5 8 9

plot_dendrogram(hrg)

From Dendrogram plot, it observed that there are
- major 4 four clusters are : DEU, ITA, GRA and BEL
- minor 2 clusters are : HUN, LTU

European Commodities Trading Network in Louvain Community

Clustered by Blockmodel with Structural Equivalence Approach, Lorrain and White (1971)

Block Group, K = 6

## 
## Network Blockmodel:
## 
## 
## General information:
## 
##  Equivalence function:  sedist 
##  Equivalence metric:  hamming 
##  Clustering method:  complete 
##  Blockmodel content:  density 
## 
## 
## Block membership by actor:
## 
## AUT BEL BGR CYP CZE DNK EST FIN FRA DEU GRC HUN ISL IRL ITA LVA LTU LUX 
##   1   2   1   1   1   3   3   3   4   5   1   1   1   1   6   1   1   2 
## MLT NLD NOR POL PRT ROU SVK SVN ESP SWE CHE GBR 
##   1   2   3   1   2   1   1   1   2   3   2   4 
## 
## 
## Block membership by block:
## 
##   Block 1 : GRC ROU BGR CYP CZE SVK AUT HUN SVN ISL IRL MLT LVA LTU POL 
##   Block 2 : CHE PRT ESP BEL LUX NLD 
##   Block 3 : SWE DNK NOR EST FIN 
##   Block 4 : FRA GBR 
##   Block 5 : DEU 
##   Block 6 : ITA 
## 
## 
## Reduced form blockmodel:
## 
##   AUT BEL BGR CYP CZE DNK EST FIN FRA DEU GRC HUN ISL IRL ITA LVA LTU LUX MLT NLD NOR POL PRT ROU SVK SVN ESP SWE CHE GBR 
##            Block 1    Block 2    Block 3    Block 4 Block 5   Block 6
## Block 1 0.06666667 0.03333333 0.01333333 0.06666667     0.8 0.4666667
## Block 2 0.00000000 0.20000000 0.00000000 0.91666667     1.0 0.6666667
## Block 3 0.09333333 0.16666667 0.70000000 0.70000000     1.0 0.2000000
## Block 4 0.16666667 0.75000000 0.20000000 1.00000000     1.0 1.0000000
## Block 5 0.93333333 1.00000000 1.00000000 1.00000000     NaN 1.0000000
## Block 6 0.60000000 0.66666667 0.00000000 1.00000000     1.0       NaN
## 
## 
## Blocked data:
## 
##   AUT BEL BGR CYP CZE DNK EST FIN FRA DEU GRC HUN ISL IRL ITA LVA LTU LUX MLT NLD NOR POL PRT ROU SVK SVN ESP SWE CHE GBR 
##     DEU ITA FRA GBR SWE DNK NOR EST FIN CHE PRT ESP BEL LUX NLD GRC ROU
## DEU   0   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
## ITA   1   0   1   1   0   0   0   0   0   1   1   1   1   0   0   1   1
## FRA   1   1   0   1   1   0   0   0   0   1   0   1   1   1   1   0   0
## GBR   1   1   1   0   1   0   0   0   0   1   0   1   1   0   1   0   0
## SWE   1   1   1   1   0   1   1   1   1   0   0   0   0   0   1   0   0
## DNK   1   0   0   1   1   0   1   0   0   0   0   0   0   0   0   0   0
## NOR   1   0   0   1   1   0   0   0   0   0   0   0   0   0   1   0   0
## EST   1   0   0   1   1   1   0   0   1   0   0   0   0   0   0   0   0
## FIN   1   0   1   1   1   1   1   1   0   0   0   1   1   0   1   0   0
## CHE   1   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0
## PRT   1   0   1   1   0   0   0   0   0   0   0   1   0   0   0   0   0
## ESP   1   1   1   1   0   0   0   0   0   0   1   0   0   0   0   0   0
## BEL   1   1   1   1   0   0   0   0   0   0   0   0   0   1   1   0   0
## LUX   1   1   1   0   0   0   0   0   0   0   0   0   1   0   0   0   0
## NLD   1   1   1   1   0   0   0   0   0   0   0   0   1   0   0   0   0
## GRC   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## ROU   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0
## BGR   0   1   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0
## CYP   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   1   0
## CZE   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## SVK   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## AUT   1   1   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0
## HUN   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## SVN   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## ISL   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## IRL   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
## MLT   1   1   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0
## LVA   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## LTU   1   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0
## POL   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##     BGR CYP CZE SVK AUT HUN SVN ISL IRL MLT LVA LTU POL
## DEU   1   1   1   1   1   1   1   1   0   1   1   1   1
## ITA   1   1   0   1   0   1   1   0   0   1   0   0   1
## FRA   0   0   0   0   0   0   1   0   0   0   0   0   0
## GBR   0   1   0   0   0   0   0   1   1   1   0   0   0
## SWE   0   0   0   0   0   0   0   1   0   0   1   0   0
## DNK   0   0   0   0   0   0   0   1   0   0   0   1   0
## NOR   0   0   0   0   0   0   0   1   0   0   0   0   0
## EST   0   0   0   0   0   0   0   0   0   0   1   0   0
## FIN   0   0   0   0   0   0   0   0   0   0   1   0   0
## CHE   0   0   0   0   0   0   0   0   0   0   0   0   0
## PRT   0   0   0   0   0   0   0   0   0   0   0   0   0
## ESP   0   0   0   0   0   0   0   0   0   0   0   0   0
## BEL   0   0   0   0   0   0   0   0   0   0   0   0   0
## LUX   0   0   0   0   0   0   0   0   0   0   0   0   0
## NLD   0   0   0   0   0   0   0   0   0   0   0   0   0
## GRC   1   1   0   0   0   0   0   0   0   0   0   0   0
## ROU   0   0   0   0   0   0   0   0   0   0   0   0   0
## BGR   0   0   0   0   0   0   0   0   0   0   0   0   0
## CYP   0   0   0   0   0   0   0   0   0   0   0   0   0
## CZE   0   0   0   1   0   0   0   0   0   0   0   0   0
## SVK   0   0   1   0   0   0   0   0   0   0   0   0   1
## AUT   0   0   0   0   0   1   1   0   0   0   0   0   0
## HUN   0   0   0   0   1   0   0   0   0   0   0   0   0
## SVN   0   0   0   0   1   0   0   0   0   0   0   0   0
## ISL   0   0   0   0   0   0   0   0   0   0   0   0   0
## IRL   0   0   0   0   0   0   0   0   0   0   0   0   0
## MLT   0   0   0   0   0   0   0   0   0   0   0   0   0
## LVA   0   0   0   0   0   0   0   0   0   0   0   0   0
## LTU   0   0   0   0   0   0   0   0   0   0   1   0   0
## POL   0   0   0   0   0   0   0   0   0   0   1   1   0

	Block 1	Block 2	Block 3	Block 4	Block 5	Block 6
Block 1	0.067	0.033	0.013	0.067	0.8	0.467
Block 2	0.000	0.200	0.000	0.917	1.0	0.667
Block 3	0.093	0.167	0.700	0.700	1.0	0.200
Block 4	0.167	0.750	0.200	1.000	1.0	1.000
Block 5	0.933	1.000	1.000	1.000	NaN	1.000
Block 6	0.600	0.667	0.000	1.000	1.0	NaN
Note:
mynet_dir_04_SED, Structural Equivalent, Reduced Form
¹ NA = self tie of its own Country (undefined)

Blondel, Vincent D., Jean-Loup Guillaume, Renaud Lambiotte, and Etienne Lefebvre. 2008. “Fast Unfolding of Communities in Large Networks.” Journal of Statistical Mechanics: Theory and Experiment 2008 (10): P10008. https://doi.org/10.1088/1742-5468/2008/10/p10008.

Lorrain, Francois, and Harrison C White. 1971. “Structural Equivalence of Individuals in Social Networks.” The Journal of Mathematical Sociology 1 (1): 49–80. https://doi.org/10.1016/b978-0-12-442450-0.50012-2.

Commodities Trading Network in Europe: R + igraph +SNA + network

Written by DK