Abstract The landscape in the world trade network has changed in last few decades.  This paper analyses World Trade Network (WTN) from 1990 to 2016, using the trade data available at the International Monetary Fund (IMF) website and presents the evolution of key players in the network using link analysis properties. Link Analysis analyzes the link strength between nodes of a network to evaluate the properties of the network. The paper uses link analysis algorithm such as PageRank, hubs, and authority to evaluate the strength or importance of nodes in the World Trade Network. A higher PageRank represents higher import dependencies, higher authority scores of a country denotes its significance to import from other hub countries, and a higher hub score indicates a country’s significance to export their final product to other authority sectors. The findings show the emergence of Asian countries, especially China, as key players in the world.  Key Words: World Trade Network, link analysis, PageRank, Authority, Hubs Introduction The value of global total export in the year 2016 is almost five (4.96) times the value in the year 1990. This fivefold growth in trade value is largely contributed by Emerging Market Economics (EMEs) \cite{Riad2012}. This indicates trade plays a vital role in the national economy as well as in the international economy. In this context, studying world trade from complex network perspectives provides meaningful insights. World Trade Network (WTN) is weighted directed complex network of countries around the world. In network science, a network is a collection of nodes and links, links are relations between the nodes and, in graph theory, a graph is a collection of vertices and edges, where edges are a relationship between vertices. Graph and Network are terms used interchangeably in this paper. For the WTN nodes are represented by the countries around the world and link represents the relationship between two countries, where the relationship is a flow of trade from one country to another. Study of the WTN applying network and graph theory framework has been growing and could be found in these works of literature \cite{Reyes2014,Deguchi2014}  \cite{Ermann2011,Benedictis2010}. This paper uses link analysis algorithms to analyze the WTN. Link analysis extracts information from a connected structure like the WTN \cite{Chakraborty}. Understanding such connected structure of trade furnish an immense source of information about the world economy, and this paper uses approaches, which was initially adopted to understand the World Wide Web (WWW) \cite{Kleinberg1999}. Link analysis methods are also used to identify the expert in Social Network \cite{Kardan2011}. This paper Link analysis algorithms HITS (Hypertext Induced Topic Search) \cite{Kleinberg1999}and PageRank \cite{Page1998} algorithms are used to find the importance of countries based on the value export amount from one country to another. HITS and PageRank are also among the most frequently cited web information retrieval algorithms (Langville & Meyer, 2005). Link Analysis of the WTN gives importance value to the countries of the WTN.  This paper study and analyze the WTN data from 1990 to 2016 as a weighted-directed network. Using the graph framework and applying link analysis perspectives, the paper tries to figure out the emerging countries and their evolution during the study period. The following section describes the link analysis algorithms used in the study and the subsequent section describes and discusses the finding.Hits Algorithm HITS algorithm is also known as hubs and authorities algorithm (Kleinberg, 1999). This algorithm gives hubs and authority ranking for each member of the network. Hubs score of a node represents the sum of the authority score of all of the nodes which are pointing to this node. The authority score represents the sum of the hub score of all nodes pointing to this node. Hubs and authorities exhibit a mutually reinforcing relationship: a good hub is a node that points to many good authorities; a good authority is a node that is pointed to by many good hubs (Kleinberg, 1999). In the WTN hubs are countries with large export value and export to good authority countries, and authority is a country with large import values and import from good hubs countries.  

ABSTRACT Preferential trade agreements are meant to promote trade within the targeted region. Once such agreements are put into effect, it is interesting to investigate the impact and effectiveness in the targeted region. This paper analyzes world trade network as a graph and introduces the measure to evaluate a change in strength or degree of regional integration. The measure or index introduced also captures the contribution of member countries in the regional integration. INTRODUCTION The Number of preferential trade agreements has been increasing since the 1990s and has increased more than four-fold . Do preferential trade agreements foster trade between the member countries? This question has been as important today as it was when such agreements were formed. This paper analyzes world trade network data to answer this question. The main aim of such agreements is to foster mutual trade in the region and they are considered helpful for promoting the regional economic competitiveness as well. Whereas the impact of such agreements is not homogeneous across countries, the impact is large for industrialized nations and small for developing nations. Several measures of regional integration are devised and found in the literature . Intra-regional trade share ( Si ) measures the ratio of regions i intra-regional trade to total trade . Intraregional Trade Share, Intraregional Trade Intensity Index, and Regional Trade Introversion Index measure the degree of trade interdependence in a certain region . This paper analyze Regional Trade Integration Index and introduce an index, which measures the individual contribution of member countries in the given region. METHODOLOGY This paper introduces an index to study regional trade integration and examines trade data before and after the formation of such agreements. Collection of countries around the world and their trade relationship is represented by graph G(W, E) . W represents a set of all countries and E represents a set of all directed edges or all possible exports. Let eij represents the amount of export from country i to j country. REGIONAL TRADE INTEGRATION INDEX (RTII): This index is the ratio of the sum of exports of all member nations within the region to the sum of export of member nations outside the region. The index range from 0 to 1. Index 0 indicates the member countries do not export within region index 1 indicates the members in a group export everything to other group members. Let g(W′, E′) be a subgraph of G(W, E) and W′ ⊆ W and E′ ⊆ E. In real world, graph G(W, E) all countries in the world and their export relationship. And, subgraph g(W′, E′) represent some preferential trade agreements e.g. NAFTA. Regional Trade Integration Index (RTII) for subgraph g is calculated as Ig. $$I_g=}}e_{ij}}} {}e_{ij}}$$ Individual contribution to the regional integration is computed as Individual Contribution Index (ICI) $$ICI_g^{i}=}e_{ij}}} {}e_{ij}}$$ Where, ICIgi is the ICI for a country i in subgraph g. The weighted sum of Individual Contribution Index is equal to Regional Trade Integration Index . $$I_g = \sum}ICI_g^{i}$$ INDIVIDUAL TRADE INTEGRATION INDEX (ITII): The index indicates how integrated a country is in a certain or group. The index compares the country’s export within the region to export outside the region. Or, the index calculates the ratio of the sum of the export of a country to all another member country in a region to the sum of export of the country to all nations around the globe. This index range from 0 to 1. Integration index 0 indicates the country export within the region is 0 or the country doesn’t export at all to the member countries in the region. Integration index 1 indicates the country’s whole export is within the region and exports nothing outside the region. This paper introduces an integration index Igi, which represents the integration of a country i in some region g or trade agreement or subgraph is given by $$I^{i}_{g} = }{e_{ij}}}{\sum{e_{ij}}}$$ DISCUSSION This paper analyzes and investigates the trend of regional integration for regional trade agreements NAFTA. The ITII of a country with respect to a particular region indicates the country’s contribution to regional integration and RTII represents a ratio of the region’s export within the same region to export to all other countries. Figure [109874] shows RTII for the NAFTA region and the ITII for all countries in the that region. The figure shows RTII for the NAFTA region is almost at the same level in 1990 and 2016 with some fluctuations in between. RTII shown by the red solid line in the figure indicates, the percentage of trade export that NAFTA does within the region compared to all around the world. The RTII trend indicates gradual increment from the inception of NAFTA to downward trend particularly during the global financial slowdowns around the year 2008. The RTII was 0.430114 when the group was formed and reached up to 0.576939 in 2002, then decreased to 0.487429 in 2009, eventually follows an increasing trend after the financial crisis of 2008. Downward trend before 2008 and the upward trend after 1999 is noticeable. If we look at the individual countries ITII, Mexico’s the ITII index is highest among the three countries followed by Canada and the USA. Notably, the ITII is moving parallel for three nations.