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Análisis clúster de la red de comercio internacional entre 1992 y 2015.

&= nbsp;

Cluster analysis of the network of international trade between 1992 and 2015.

Víctor Roberto Morales-Ońate.[1] & Bolívar Efraín Morales-Ońate. [2]. <= /o:p>

Recibido: 17-07-2017 / Revisado: 10-09-2018 Aceptado: 08-10-2018/ Publicado: 01-11-2018=

DO= I: https://doi.org/10.33262/cienciadigital.v2i4.1.= .188

Abstract= . =

Cluster analysis is a tool used in various fields of research that allow structural evidence in the configuration of groups. International trade networks, on t= he other hand, can be analyzed in terms of graph theory. This article combines both perspectives in such a way that the links of a trade network can be analyzed. Powerful results have been obtained for the analysis of internati= onal trade that account for the centrality of countries through their links and = not their nodes only.

Keywords: International trade network, clustering, central= ity measures.

Resumen.

El análisis clúster es una herramienta usada en diversos campos de la investigación que permite eviden= cia estructuras en la configuración de grupos. Las redes de comercio internacio= nal, por su parte, puede ser analizadas en términos de la teoría de grafos. Este trabajo combina ambas perspectivas de tal modo que se pueda analizar los enlaces de una red de comercio. Se han obtenido resultados potentes para el análisis del comercio internacional que dan cuenta de la centralidad de los países a través de sus enlaces y no únicamente sus nodos.=

Palabras Claves= :<= span style=3D'mso-bookmark:_Toc440896901'> red de comercio internacional, clustering, medidas de centralidad.

Introducción.

El comercio internacional puede ser analizado desde varias perspectivas, que varían desde un enfoque de leyes y tratados que no= rman las relaciones bilaterales y multilaterales (Gervais & Gervais, 1998; Ruse-Khan & Grosse, 20= 18; Park, 2008; Hoekman, Mattoo, & English, 2002; Matthews, 2003), hasta propuestas de análisis a través modelos. Por ejemplo, el modelo de gravitación ha sido ampliamente utilizado en la literatura de comercio internacional (Bergstrand, 1985; Mátyás, 1997; Van Bergeijk, 2010). El comercio internacional puede ser también sujeto de análisis a través de redes, ya que los flujos de comercio entre los diferentes países constituye= n en si mismo una red, por lo que se puede encontrar en la literatura numerosas referencias que analizan la red de comercio mediante teoría de redes.<= /o:p>

Este análisis de redes puede ser orientado, al men= os, de tres diferentes formas: caracterización, modelización e inferencia y procesos de redes. Asimismo, la caracterización también es abordable desde varios enfoques. Por ejemplo, a través de la caracterización de nodos y enl= aces (links por sus siglas en inglés), subgrafos o particiones de la red = (Kolaczyk & Csárdi, 2014; Françoisse, Kivimäki, Mantrach, Rossi, & Saerens, 2017; Goldenberg, Zheng, Fienberg, & Airoldi, 2010).

Tradicionalmente, la descricpión de la red se real= iza mediante indicadores descriptivos de centralidad. Las medidas de centralidad tradicionales son closenness y = betweenness, mientras que medidas = más actuales incluyen a la centralidad basada en la elasticidad país-país (Pérez-Oviedo, Cajas-Guijarro, & María, 2017). Closenness, mide la cercanía que tiene un nodo respecto a sus vecinos (Sabidussi, 1966). La versión clásica del indicado= r es la inversa respecto a una medida de distancia a otros nodos y se calcula mediante la fórmula: , donde denota la distancia entre los nodos y . Betweenness mide el grado en el que un nodo se localiza “entre” otros nodos= . Es decir, mide la importancia del vértice respecto al número de caminos del cu= al es parte. Una presentación clásica del indicador es: (Freeman, 1977). Finalmente, la elasticidad país-país supone una propensión marginal a importar, así como una determina= da estructura comercial dada por la red. En términos matriciales, el indicador= de centralidad denominado elasticidad país-país está dado por . Donde es una matriz de elasticidades que estim= a el cambio porcentual que se da en el ingreso de un país cuando se cambia en un punto porcentual = el ingreso de un país . es una matriz diagonal que contiene el <= /span> de cada país, es una matriz diagonal que recoge la propensión marginal a importar de cada país y es la matriz de flujos país-país. A partir de la matr= iz es posible calcular la media de <= /span> ponderada por la participación de cada p= aís en la producción mundial: donde denota la centralidad de cada país. Tamb= ién es posible calcular el efecto del resto del mundo sobre el país = : donde estima la dependencia de un país frente = a un shock del resto de países.

Todas las medidas de centralidad mencionadas anteriormente plantean una versión que puede ser utilizada en grafos podera= dos y dirigidos. Es justamente en el uso de las ponderaciones de los enlaces en= que se se trata de dar cuenta de la intensidad de la relación entre los nodos. = Sin embargo, hay pocos estudios que caracterizan los enlaces enlaces de un grad= o e una red de comercio, la literatura se ha priorizado el rol de los nodos y n= o de sus links (Gao, Small, & Kurths, 2017; Pokorny, y otros, 2018; McDonald & Hobson, 2018).

En términos de teoría de redes, la red de comercio internacional es una red ponderada y dirigida. La medida de elasticidad país-país toma en cuenta estas caracteríasitcas de la red y uno de sus principales resultados intermedios es la generación de una matriz de elasticidades (que puede ser vista como una matriz de enlaces). A partir de este resultado se recupera una medida de centralidad de los nodos como se ha indicado anteriormente. No obstante, el presente trabajo dirige su atención= al análisis de la matriz de enlaces en si misma. Mediante el uso de técnicas de clustering, se ha encontrado configuraciones de grupos de enlaces que permi= ten una caracterización de la red priorizando los enlaces y no los nodos. Para = este propósito ha sido necesario pasar por un importante anális descriptivo (EDA= ) de los datos con el propósito de tener una intuición profunda del conjunto y establecer, entre otras cosas, los ańos representativos mediante el uso de pruebas no paramétricas como Kruskal-Wallis y la aplicación del método clús= ter herárquico para el análisis final de la red (Everitt, Landau, & Leese, 2001; Gordon, 1999).

1= . Materiales y Métodos.

Las técnicas de clasificación se dividen en particional y jerárquica. En la primera es necesario establecer de antemano= el número de grupos que se desea obtener. La agrupación jerárquica, por su par= te, agrupa los datos con una secuencia de particiones anidadas, desde grupos ún= icos hasta un grupo que incluye a todos los individuos o viceversa. Los algoritm= os jerárquicos aglomerativos comienzan considerando grupos unitarios y proceden fusionando dichos grupos hasta lograr un sólo grupo con todos los individuos. Al considerar todo el tiempo grupos, en lugar de patr= ones individuales, los algoritmos jerárquicos requieren un criterio para compara= r, por semejanza o diferencia, grupos de patrones. Esos criterios se conocen c= omo funciones de enlace (linkage functi= ons) y existen en varias formas (Xu & Wunsch, 2008). La

Figura 1 hace referencia a las más usadas: vecino más próx= imo, promedio y vecino más lejano. Sin embargo, la función de enlace de Ward es mejor que los enfoques tradicionales para el caso en el que se realiza la aplicación de este trabajo.

Figura 1: Diferentes funciones de enlace. a. Vecino más próximo. b. Promedio (average). C. Vecino más lejano (complete) . Fuente y elaboración: autores.

Siguiendo a (Xu & Wunsch, 2008), la Figura 2 presenta el flujograma del algoritmo algomeratico jerárquico y a continuación se listan los pasos a seguir:=

Empieza c= on = grup= os. Calcula la matriz de proximidad (de semejanza o diferencia) para los <= /span> = grup= os.
En la mat= riz de proximidad busca la distancia mínima = dond= e = es u= na función de distancia que combina los grupos = y = para formar un nuevo cluster = .
Actualiza= la matriz de proximidad calculando las distancias entre los grupos = y los demás.
Repetir l= os pasos 2 y 3 hasta que únicamente quede un grupo.

Figura 2: Flujograma del algorit= mo algomeratico jerárquico. Fuente: (Xu & Wunsch, 2008)<= span lang=3DES-CL style=3D'font-size:12.0pt;line-height:115%;font-family:"Times = New Roman",serif; mso-ansi-language:ES-CL;mso-bidi-font-style:italic'>. Elaboración: autores.=

Claramente, la función de distancia es crucial par= a la unión de dos grupos. Existen varias definiciones de distancias para realizar dicha unión. Entre las más utilizadas tenemos (Everitt, Landau, & Leese, 2001)

Vecino más cercano: la distancia entre un par de grupos está determinada por los = dos objetos más cercanos a los diferentes grupos (ver
Figura 1a).Sin pérdida de generalidad, sean = y = un p= ar de grupos cualesquiera. Entonces, = dond= e = es u= na función de semejanza o diferencia.
Promedio:= La distancia entre dos grupos se define como el promedio de la distancia entre todos los pares de puntos de datos, cada uno de los cuales provi= ene de un grupo diferente (ver figura
Figura 1b). Sin pérdida de generalidad, sean <= /span> = y = un p= ar de grupos cualesquiera. Entonces, = dond= e = deno= ta la cardinalidad del conjunto y = es u= na función de semejanza o diferencia.
Vecino más lejano: utiliza la distancia más alejada de un par de objetos a una distancia entre grupos definida (ver
Figura 1c). Sin pérdida de generalidad, sean <= /span> = y = un p= ar de grupos cualesquiera. Entonces, = dond= e = es u= na función de semejanza o diferencia. Esta función de enlace es particularmente útil para encontrar grupos pequeńos y compactos.<= /o:p>
Ward: tam= bién conocido como el método de varianza mínima. La distancia entre dos gru= pos se basa en la la distancia euclideana entre sus centroides^{^[3]} y multiplicado por un factor,
= . El objetivo de la distancia de Ward es minimizar el incremento del error cuadrático dentro del grupo dado por= = .

Nuestro análisis parte de los resultados obtenidos= en (Pérez-Oviedo, Cajas-Guijarro, & María, 2017)= . Su trabajo contiene una propuesta para medir la centralidad de los países. = En términos de redes, se realiza una metodología de medición de centralidad de= una red ponderada y dirigida que caracteriza a los nodos de la red. Con este objetivo calculan una matriz de elasticidad país-país, exógenamente se asig= na un shock en el ingreso de un país, lo que incrementa las importaciones de e= se país, y tiene efectos sobre toda la red. Luego combinan esta información co= n el PIB de los países de la red para obtener el indicador de centralidad de cada país. El presente trabajo, por otra parte, caracteriza la matriz de elastic= idad país-país. Es decir, se usa esta matriz para cada ańo del período 1992-2015 para analizar sus enlaces desde una perspectiva de clusters.

Figura 3: Densidad empírica de la elasticidad para el período 1992-2015. Fuente: (Pérez-Oviedo, Cajas-Guijarro, & María, 2017)= . Elaboración: autores.

La primera pregunta que exploramos en esta sección= es la estructura de la elasticidad calculada para cada par de países en el per= íodo de estudio. Se desea establecer si ha existido cambios significativos en di= cha estructura. El rango de la elasticidad se encuentra en el intervalo de a = para todo= el período y, como se puede apreciar en la Figura 3 su distribución es marcadamente asimétrica. Por lo tanto, se realiza un gráfico de la densidad empírica del logaritmo de la elasticidad para cada ańo (

Figura 4).

&nbs= p;

Figura 4: Densidad de la elastic= idad por ańo para el período 1992-2015. Fuente: (Pérez-Oviedo, Cajas-Guijarro, & María, 2017)= . Elaboración: autores.

Contrariamente al comportamiento de la variable en niveles, la

Figura 4 mejora la visualización de mediante la transforma= ción logarítmica de la elasticidad. También sugiere que no se debe asumir una distribución normal si se desea analizar los datos desde un punto de vista paramétrico. Además se aprecia que la media de la distribución crece, siend= o = en 1992 y= = en el 201= 5. Una forma de explorar dichas diferencias puede ser a través de diferentes venta= nas de tiempo dentro del período analizado. Por ejemplo, el período 1992-1996 parece tener una media por debajo del período 2011-2015. =

Tabla 1<= /span>.Prueba de Kruskal-Wallis para el logaritmo de la elasticidad en el período 1992-2015. Fuente y elaboración: autores.

Ańo (i)	Ańo (j)	p-valor
1993	1994	0.17
1997	1998	0.44
1997	1999	0.97
1998	1999	0.46
2000	2001	0.84
2000	2002	0.12
2000	2003	0.84
2001	2002	0.08
2001	2003	0.67
2002	2003	0.17
2004	2009	0.06
2005	2009	0.47
2005	2010	0.08
2005	2015	0.14
2006	2007	0.14
2006	2010	0.59
2006	2015	0.41
2008	2011	0.39
2008	2012	0.39
2008	2013	0.19
2010	2015	0.79
2011	2012	0.09
2012	2013	0.65
2012	2014	0.25
2013	2014	0.48

Con el objetivo de responder más apropiadamente a = las anotaciones precedentes se han realizado pruebas de Kruskal-Wallis (KW), pa= ra todo el período, indicando que si se rechaza la hipótesis nula se trataría = de poblaciones diferentes y la variable analizada cambia durante el período analizado. Bajo este razonamiento, la tabla 1 presenta los -valores de la prueba KW realizada para cada parej= a de ańos donde no se rechaza la hipótesis nula. En base a la tabla 1,se puede apreciar que hay tres ańos que se diferencian de casi todos los demás: 1992, 1995 y 1996. Asimismo, se puede usar ańos representantes de algún período. = Por ejemplo, el ańo 2001 no presenta diferencias significativas, hacia atrás co= n el 2000, ni hacia adelante con 2002 y 2003. Por lo tanto, el ańo 2001 podría s= er considerado como un representante del período 2000-2003.<= /span>

Se ha establecido que la elasticidad analizada es = una variable asimétrica y que es apropiada una transformación logarítmica para acceder a su mejor entendimiento. Los valores mínimo, media, mediana y máxi= mo de la elasticidad transformada para todo el periodo son: <= ![if !msEquation]> , , y = . Estos valores, y las densidades empíricas de la =

Figura 4, muestran que la transformación puede considerarse como aproximadamente simétrica. No obstante, el rango de sus valores sigue siendo cercano. Por lo tanto, al explorar la elasticidad en el marco de algoritmos de clasificación, el indicador within será quien guíe la decisión del mejor algoritmo a usarse.

Recordemos que la centralidad en (Pérez-Oviedo, Cajas-Guijarro, & María, 2017)= es calculada a partir de la elasticidad y el porcentaje del PIB, luego se aplica la metodología resumida en la introducción, obteniendo una carteriza= ción de nodos. Utilizando las mismas variables para la construcción de la centralidad, este trabajo busca una caracterización de los links de la red = de comercio internacional mundial. Por lo tanto, la matriz de entrada (conjunt= o de patrones) que se ha usado en los algoritmos de clasificación está compuesta= de parejas de links en las filas (objetos) y en las columnas las variables (atributos): elasticidad, porcentaje de PIB del país de origen y destino, t= res variables en total.

Tabla 2.Estadísticos de clasificación para los ańos referencia: 1993, 2001 y 2015. Fuente: y elaboración: autores.

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Ańos	<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Algortimo	<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Within	<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Between
1993	Single	0.626	9.151
Complete	0.48	8.163
Average	0.505	8.442
Ward	0.088	1.506
2001	Single	0.624	11.644
Complete	0.541	8.792
Average	0.589	11.093
Ward	0.105	1.352
2015	Single	0.772	10.453
Complete	0.573	8.307
Average	0.582	8.393
Ward	0.12	1.355

La Tabla 2 muestra los estadísticos de clasificación within y between que usan una métrica de distancia dentro de los grupos y entre grup= os respectivamente. Se puede apreciar que el algoritmo de Ward es el que prese= nta mayor cercanía dentro de los clusters, lo cual es deseable en nuestro caso debido al bajo rango de las variables de entrada. Por lo tanto, para la caracterización de los links se hace uso del algoritmo de Ward, con esta elección de algoritmo analizamos tres ańos de referencia (1993, 2001 y 2015) desde un enfoque temporal de la clasificación jerárquica donde se realiza u= na evaluación más exhaustiva.

2. Resultados.

Como se ha mencionado, existen propuestas de clasificación que tienen por objeto darle más énfasis a heterogeneidad entre grupos, por lo que el indicador between es el que guía la clasificación (Newman & Girvan, 2004). Este trabajo, por otro lado, guía la clasificación apoyándose en el indicad= or within, siendo el método Ward el más apropiado para nuestro análisis. =

Figura 5: Dendogramas de los ańos 1993, 2001 y 2015 (de izquierda a derecha). Fuente y elaboración: autores.<= o:p>

Figura 5<= /i> presenta los clusters jerárquicos para los ańos seleccionados para el análisis. Se puede apreciar que existe un cambio de estructura en los dendogramas a través del tiempo, principalmente entre 199= 3 y 2001. Las líneas en rojo muestran el corte de cada dendrograma de modo que = se generen cinco grupos de links para cada ańo. La Figura 6 muestra la frecuencia de links que pertenecen a c= ada uno de los grupos. Existe homogeneidad en cuanto al número de links por gru= pos en cada ańo. Además, la Tabla 3 muestra el valor de la elasticidad utilizada en la agrupación jerárquica.

Tabla 3.Mediana del logaritmo de la elasticidad normalizada para los ańos 1993, 2001 y 2015. Fuente y elaboración: autores.<= /span>

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Ańo

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Grupo 1

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Grupo 2

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Grupo 3

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Grupo 4

<= span lang=3DES-CL style=3D'font-size:10.0pt;line-height:115%;font-family:"Time= s New Roman",serif; mso-ansi-language:ES-CL'>Grupo 5

1993

−0.169

0.202

2.779

−0.167

−0.167

2001

−0.182

0.29

2.974

−0.179

−0.182

2015

−0.198

0.328

1.455

−0.190

−0.191

Figura 6: Número de enlaces por = ańo y grupo. Fuente y elaboración: autores.

Con esta información, la jerarquía de los grupos en orden descendiente es: 3, 2, 4, 5 y 1. Para caracterizar los grupos, la Tabla 4 muestra la frecuencia con la que se repite los ci= nco primeros país de origen y destino en los grupos 1, 3 y 5. El grupo 3, que e= s el de mayor importancia, parte en 1993 con Japón, Estados Unidos, Gran Bretańa= y Francia como los países de mayor frecuencia. Luego en 2001, aparecen en el = top 5 China y Espańa, desplazando a Francia y Gran Bretańa. Después, en 2015 se quedan Estados Unidos y China como los únicos países que aparecen como país= es de destino en este grupo. El grupo 5, que es el penúltimo en importancia, p= arte en 1993 con Japón y Estados Unidos como los únicos países que aparecen como origen. En 2001 tan solo se queda Estados Unidos en esa condición. Luego, en ańo 2015, China pasa a acompańar a Estados Unidos en este grupo.=

Tabla 4.Frecuencia los cinco países de mayor repetición de origen y destino en cada grupo para los ańos 1993, 2001 y 2015. Fuente y elaboración: autores.

1993

G1

Destino=

País

BLR

DOM

HTI

KAZ

KGZ







Frecuen= cia

120

120

120

120

120





Origen =

País

POL

FIN

IDN

ARG

AUT







Frecuen= cia

119

116

116

115

114



G3

Destino=

País

SGP

MYS

NGA

SUR

BEL







Frecuen= cia

12

9

8

8

7





Origen =

País

JPN

USA

GBR

DEU

FRA







Frecuen= cia

133

133

26

23

23



G5

Destino=

País

JPN

USA













Frecuen= cia

132

132





   =





Origen =

País

ALB

ARG

ARM

ATG

AUS







Frecuen= cia

2

2

2

2

2

2001

G1

Destino=

País

BTN

HTI

KNA

NPL

PLW







Frecuen= cia

120

120

120

120

120





Origen =

País

ALB

ARM

ATG

AZE

BDI







Frecuen= cia

118

118

118

118

118



G3

Destino=

País

GNQ

ATG

BLR

BRN

HUN







Frecuen= cia

3

2

2

2

2





Origen =

País

USA

DEU

JPN

CHN

ESP







Frecuen= cia

133

2

2

1

1



G5

Destino=

País

USA







   =







Frecuen= cia

133







   =





Origen =

País

ALB

ARG

ARM

ATG

AUS







Frecuen= cia

1

1

1

1

1

2015

G1

Destino=

País

BDI

BGD

BTN

GMB

GRD







Frecuen= cia

118

118

118

118

118





Origen =

País

ALB

ATG

AZE

BDI

BHS







Frecuen= cia

118

118

118

118

118



G3

Destino=

País

ALB

ARG

ARM

ATG

AUS







Frecuen= cia

2

2

2

2

2





Origen =

País

USA

CHN













Frecuen= cia

129

123







G5

Destino=

País

CHN

USA











Frecuen= cia

132

132









Origen =

País

ALB

ARG

ARM

ATG

AUS







Frecuen= cia

2

2

2

2

2

Habiendo obtenido los conglomerados generados a pa= rtir de los enlaces de la red de comercio internacional, es natural analizar esta configuración en términos de su evolución. La Figura 7 muestra los enlaces de la red dividio en grupos p= ara los ańos 1993, 2001 y 2015. Se aprecia que la estructura económica del 2001 difiere considerablemente de los demás ańos. Por ejemplo, el grupo 3 deja de tener fuerza en Rusia y el grupo 1 toma el liderazgo. Tambíen se aprecia qu= e el grupo 2 gana mercado paulatinamente en los ańos analizados.

Figura 7: Evolución de la red de comercio internacional dividida en clusters. De arriba habia abajo: 1993, 2= 001 y 2015. Fuente y elaboración: autores.

Otro contraste interesante de los grupos obtenidos= se presenta en la Figura 8, esta vez poderando los enlaces en función de sus valores de elasticidad. Consecuentemente con el análisis anterior, el grupo= 3 nuevamente gana mercado en la evolución. Se aprecia un efecto de incremento= en las relaciones comerciales entre América y los demás continentes, presumiblemente un efecto esperado de la globablización. Asimismo es posible apreciar un comportamiento similar del grupo 1 entre el 2001 y el 2015. Cabe notar que el grupo 1 era el más sobresaliente en la Figura 7, sin embargo, al tomar en cuenta la ponderación de los enlaces, su importancia se ve afectada.

Figura 8: Evolución de la red de comercio internacional dividida en clusters y ponderada por elasticidad. De arriba habia abajo: 1993, 2001 y 2015. Fuente y elaboración: autores.<= /o:p>

Finalmente, la Figura 9 presenta al grupo 5 aisaldo del resto para poder apreciar su evolución de forma expedita. Se aprecia como nodos centrales a Estados Unidos y Japón en el 1993. Luego, en el 2001 Japón pierde relevancia dentro del grupo pero la recupera, aunque no con la misma intensidad, para = el 2015. Respecto a 1992, el ańo 2015 muestra relaciones que previamente no se habían establecido. Por ejemplo, se han generado varios enlaces comerciales= con países africanos. Además, es notable la centralidad que ocupa China para el= 2015 luego que Japón ha perdido relevancia en este grupo de enlaces.

Figura 9: Evolución del grupo 5 = en la red de comercio internacional. De arriba habia abajo: 1993, 2001 y 2015. Fuente y elaboración: autores.

3.      Discusión.

Una de las innovaciones = del presente trabajo es el campo de aplicación de las técnicas clúster. Precisamente, en el contexto del análisis de la matriz de las elasticidades país-país y su configuración de grupos legibles en la evolución de la red de comercio internacional. Por este motivo, esta aplicación puede servir de in= sumo para analistas económicos de comercio internacional de modo que puedan dar evidencia de las estructuras de comercio a las que están ancladas los diferentes países del mundo. Ubicando las centralidades desde una perspecti= va del enlace y no únicamente desde los nodos analizados.

=

Es claro que las consideraciones aquí tomadas pueden tener otros abordajes. Por ejemplo, la configuración de grupos es siempre un debate abierto en la literatura estadística. Se podría incluir variables nominales u ordinales como la presencia o no de pactos bilaterales entre países lo cual podría re configu= rar los grupos y dar evidencia de nuevas alianzas entre países. También sería posible variar la técnica de cluster, pasando del enfoque jerárquico aquí presentado y orientar la investigación a travéz de clasificaciones superviz= adas y no supervizadas no jerárquicas. La selección de los ańos para la intuició= n de la evolución de la red tamibén admite técnicas de otro tipo. Por ejemplo, en cada ańo i) se podría estimar la función de distribución acumulativa empíri= ca (ecdf), ii) generar números aleatorios usando el método de transformación inversa y, iii) un determinado número de réplicas de indicadores de centralidad y así tener la estimación de la ecdf de cada país. Los pasos anteriores podrían permitir realizar pruebas no paramétricas para determinar si existen diferencias significativas en las medidas de centralidad de los países.

=

Pese a las posibles particularidades que susceptibles de modificación en el proceso que se ha seguido, claramente este trabajo es una invitación a la exploración y aplicación de técnicas que permitan dar cuenta de la estructura de la red de comercio. En este sentido, se ha planteado una meta metodología: dada una ventana de tiempo de una red de comercio, i) resaltar las variaciones anual= es y así seleccionar ańos relevantes de la ventana de tiempo, ii) seleccionar una técnica cluster adecuada para clasificar enlaces de una red, y ii) presentar evolutivamente los resultados en forma de mapas que den cuenta de la interacción de los resultados con las centralidades de los nodos.

Agradecimiento.

Los autores agradecen la colaboración de Wilson Pérez-Oviedo y John Cajas-Guijarro en el desarrollo del presente trabajo.

<= /o:p>

<= /o:p>

Referencias bibliográficas.

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Matthews, d. (2003). Globalising intellectual property rights: the trips agreement.= Routledge.

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Van bergeijk, = p. A. (2010). The gravity model in international trade: advances and applications. Cambridge university press.

Kolaczyk, e. D= ., & csárdi, g. (2014). Statistical analysis of network data with r (vol. 65). Nueva york: springer.

Françoisse, k., kivimäki, i., mantrach, a., rossi, f., & saerens, m. (2017). A bag-of-paths framework for network data analysis. Neural networks, 90<= /i>, 90-111.

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Pokorny, j. J., norman, a., zanesco, a. P., bauer-wu, s., sahdra, b. K., & saron, c. = D. (2018). Network analysis for the visualization and analysis of qualitative data. Psychological methods, 23(1), 169.<= /p>
Mcdonald, d. B= ., & hobson, e. A. (2018). Edge weight variance: population genetic metr= ics for social network analysis. Animal behaviour, 136, 239-250.<= /o:p>

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Newman, m. E., & girvan, m. (2004). Finding and evaluating community structure in networks. Physical review e, 69(2).

Pérez-oviedo, = w., cajas-guijarro, j., & maría, v. (2017). South america: trade and integration in the new global trade network. En e. Vivares, regionalis= m, development and the post-commodities boom in south america (págs. 121-145). Estados unidos: springer.

Goldenberg, a., zheng, a. X., fienberg, s. E., & airoldi, e. M. (2010). A survey of statistical network models. Foundations and trends in machine learning= , 2(2), 129-233.

=

Para citar el artículo indexado.<= o:p>

Morales-Ońate V., Morales-Ońate B. (2018). Análi= sis Cluster de la Red de Comercio Internacional entre 1992 y 2015. Revista electrónica Ciencia Digital 2(4), 23-41. Recuperado desde: http://cienciadigital.o= rg/revistacienciadigital2/index.php/CienciaDigital/article/view/188/166

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Ciencia Digital.

El articulo queda en propiedad de= la revista y, por tanto, su publicación parcial y/o total en otro medio tiene = que ser autorizado por el director de la Revista Ciencia Digital.

[1] Facultad Latinoamericana de Ciencias Soc= iales, Departamento de Desarrollo, Ambiente y Territorio, Quito,    Ecuador, victor.morales@uv.cl

[2]Escuela Superior Politécnica = de Chimborazo, Facultad de Ciencias, Riobamba, Ecuador, bolivar.morales@espoch.edu.ec

[3] El centroide de un grupo se define como un punto en el espacio -dimensional que se encuentra al promediar los valores de medición a lo largo de cada dimensión (variable). = Por ejemplo, su -ésima coordenada es , donde representa el conjunto de índices del gr= upo (que contiene objetos). Así, el centroide del grupo está dado por .

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//////////////////////////////////////////////////////////////////////////// //////8AAAAAAAAAAP///wAAAP////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////wAAAAAAAAAAAP///wAAAAAAAAAAAP///wAAAAAAAAAAAP///wAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAA AP///////wAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAP// /wAAAP///////wAAAAAAAAAAAAAAAP///wAAAAAAAP///wAAAP///wAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAP///wAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAP///////wAAAP///wAAAAAAAP///wAAAAAAAAAAAAAAAP///wAAAP////// /wAAAAAAAAAAAAAAAP///////wAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAP///////wAA AAAAAAAAAAAAAP////////////////////////////////////////////////////////////// /////////////////////////////////////////wAAAAAAAAAA////AAAA//////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////AAAAAAAAAAAA////AAAAAAAAAAAA ////AAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA//////// AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAAAAAAAAAA////AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAA////////AAAAAAAAAAAAAAAA////AAAAAAAA ////AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAA AAAA////AAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAA////AAAAAAAA ////AAAAAAAAAAAAAAAA////AAAA////////AAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAA AAAA////AAAAAAAAAAAAAAAA////////AAAAAAAAAAAAAAAA//////////////////////////// //////////////////////////////////////////////////////////////////////////// AAAAAAAAAAD///8AAAD///////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAD///////////8AAAD///////////////////////////////// //8AAAD///8AAAD///////////////////////////////////////8AAAD///////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////wAAAAAA AAAA////AAAA//////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// AAAA////////AAAA////////////////////////////////////AAAA//////////////////// ////////AAAA////AAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////AAAAAAAA//////////////////////////////////////////////////////////////// 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/////////////////////////////////////////////////////////////////////wAAAAAA AAAAAAAAAAAAAAAAAP///wAAAAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAP////// /////wAAAAAAAAAAAAAAAAAAAP///wAAAP///wAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAA AP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAP///wAAAP// /wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///wAAAAAAAAAAAAAAAP///////////wAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////wAAAAAAAAAAAAAA AAAAAAAAAP///////wAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////wAAAAAAAAAAAAAAAP///wAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAP///////////wAAAAAAAAAAAP///wAAAAAAAAAAAP////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAAAAAAAA////AAAA//////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////AAAA//////////////////////////////////////////// AAAA////////////////////AAAA//////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAAAAAAAAAP///wAAAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////wAAAP////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAAAAAP////////////////// /////////////////////////////////////////////////////wAAAAAAAP///////////wAA AP////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////wAAAAAAAAAA////AAAA//////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAA////////AAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAA////////////////AAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA ////AAAA////////////AAAAAAAAAAAA////AAAAAAAA////////////AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAA AAAAAAAA////AAAA////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////AAAAAAAAAAAA ////AAAA////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAA////AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////AAAAAAAAAAAAAAAA//////////////////////// //////////////////////////////////////////////////////////////////////////// ////////AAAAAAAAAAD///8AAAD///////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////AAAAAAAAAAD///8AAAD///////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAAD///////////////////////////////////////////// //////////////////////////////////////////////8AAAAAAAD///////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////wAAAAAAAAAA////AAAA //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////AAAAAAAAAAD///8AAAD///////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAAAAAD///8AAAAAAAAAAAD///8AAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAD///////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAAAAAAAAAP///wAAAP////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////wAAAAAAAP///wAAAAAA AAAAAP///wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////wAAAAAAAAAA////AAAA//////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////AAAAAAAA//////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAAAAAAAAAP///wAAAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////wAAAAAAAAAA////AAAA//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////AAAA 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAAAAAAAA ////AAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////AAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAAAAAAAAAP///wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////wAAAAAAAAAA////AAAA//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////AAAAAAAAAAD///8AAAD///////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAAAAAAD///////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////wAAAAAAAAAA////AAAA//// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAA//////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AAAAAAAAAP///wAAAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wAAAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8AAAAAAAAAAP// /wAAAP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAP////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////8AAAAAAAAAAP///wAAAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /wAAAAAAAAAA////AAAA//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////AAAAAAAAAAD///8AAAD///////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////8AAAAA 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAAAAAAAAAP///wAAAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////wAAAP///wAAAP////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////7J6AP////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////7J6AAAAAAAAAAAA////AAAA //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////AAAAAAAAAAAAAAAA////AAAA////snoA////snoAsnoAsnoAsnoAsnoA//////// snoAsnoAsnoAsnoAsnoAsnoA////snoAsnoAsnoAsnoAsnoAsnoA////////snoA////snoAsnoA ////snoA////snoA////snoA////snoA////snoAsnoA////snoA////snoA////snoA////snoA 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////wAAAAAAAAAA////AAAA//////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////AAAAAAAAAAD///8AAAD///////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAAAAAAAAAP///wAAAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAAAAAAAAAP///wAAAP////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////wAAAAAAAAAA ////AAAA//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////8AAAAAAAAAAP///wAA AP////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////72BT/// /72BT72BT////72BT////72BT72BT72BT////////////72BT////72BT////////72BT72BT/// /////72BT////72BT72BT////72BT////72BT////72BT////72BT72BT////72BT72BT72BT72B T////72BT////////72BT////72BT////////72BT72BT////////72BT////72BT72BT////72B T////72BT72BT72BT72BT////72BT////72BT72BT72BT////72BT////////72BT////72BT/// /////72BT72BT////////72BT////72BT////72BT72BT////72BT////72BT72BT////72BT/// /72BT72BT72BT////72BT////72BT////////72BT////72BT////////72BT72BT////////72B T////72BT72BT////72BT/////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////wAAAAAAAAAA////AAAA//////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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                                                 =                                                                       ISSN: 2602-8085

=                        Vol. 2, N°4.1, p. 23-41, octubre - diciembre, 2018

Estadística               =                                                                                                               =                         Página 18<= /span> de 18<= /span>

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1993	G1	Destino=	País	BLR	DOM	HTI	KAZ	KGZ
			Frecuen= cia	120	120	120	120	120
		Origen =	País	POL	FIN	IDN	ARG	AUT
			Frecuen= cia	119	116	116	115	114
	G3	Destino=	País	SGP	MYS	NGA	SUR	BEL
			Frecuen= cia	12	9	8	8	7
		Origen =	País	JPN	USA	GBR	DEU	FRA
			Frecuen= cia	133	133	26	23	23
	G5	Destino=	País	JPN	USA
			Frecuen= cia	132	132			=
		Origen =	País	ALB	ARG	ARM	ATG	AUS
			Frecuen= cia	2	2	2	2	2
2001	G1	Destino=	País	BTN	HTI	KNA	NPL	PLW
			Frecuen= cia	120	120	120	120	120
		Origen =	País	ALB	ARM	ATG	AZE	BDI
			Frecuen= cia	118	118	118	118	118
	G3	Destino=	País	GNQ	ATG	BLR	BRN	HUN
			Frecuen= cia	3	2	2	2	2
		Origen =	País	USA	DEU	JPN	CHN	ESP
			Frecuen= cia	133	2	2	1	1
	G5	Destino=	País	USA				=
			Frecuen= cia	133				=
		Origen =	País	ALB	ARG	ARM	ATG	AUS
			Frecuen= cia	1	1	1	1	1
2015	G1	Destino=	País	BDI	BGD	BTN	GMB	GRD
			Frecuen= cia	118	118	118	118	118
		Origen =	País	ALB	ATG	AZE	BDI	BHS
			Frecuen= cia	118	118	118	118	118
	G3	Destino=	País	ALB	ARG	ARM	ATG	AUS
			Frecuen= cia	2	2	2	2	2
		Origen =	País	USA	CHN
			Frecuen= cia	129	123
	G5	Destino=	País	CHN	USA
			Frecuen= cia	132	132
		Origen =	País	ALB	ARG	ARM	ATG	AUS
			Frecuen= cia	2	2	2	2	2