# Construction of the Belt and Road Trade Cooperation Network from the Multi-Distances Perspective
## 4 Construction of Trade Cooperation Network  
### Comprehensive Evaluation of Multiple Distances  
The results of the positive research of the expanded gravity model showed that geographic, factor endowment, and cultural and institutional distance have significant impacts on trade flows, proving the correctness of constructing a trade cooperation network from a multiple-distance perspective. Based on the results of the positive verification, we assigned weights to geographic, factor endowment and cultural and institutional distance, and improved the comprehensive index method to evaluate the comprehensive distance indices between China and the Belt and Road countries. The countries were further divided into different trade cooperation circles to lays the foundation for the design and construction of a trade cooperation network. The traditional methods used to determine the weights of indicators can be roughly divided into two categories: subjective weighting methods, such as the Analytical Hierarchy Process (AHP), the expert evaluation method, and comprehensive index method; and objective weighting methods, such as gray advantage analysis, principal component analysis, and factor analysis. The subjective weighting method is based on the rich experience of experts to determine the importance of properties, but is susceptible to human impact. The objective weighting method may result in the determined weights being inconsistent with the actual importance of the properties, although the weights may have a strong mathematical basis. Therefore, the comprehensive index method was modified based on the results of the positive verification of the gravity model to compute the comprehensive distance indices between China and the Belt and Road countries to overcome the shortcomings of both the subjective and objective weighting methods. 1. We chose 62 Belt and Road countries as samples and selected geographic, factor endowment, cultural distance, and institutional distance as four variables, so the sample matrix was \([X_{ij}]_{62\times 4}\). The data for the calculating the four distances were the 10-year means of these countries. 2. We changed all the aforementioned data into positive and dimensionless data. Based on the positive research results, we changed three variables, geographic distance, factor endowment, and cultural distance, into positive data using the reverse conversion method. To preserve the variation information of the indicators, we adopted the averaging method to change the data into dimensionless data, and obtained the matrix \([X_{ij}]_{62\times 4}\). 3. According to the positive verification results of the gravity model, \(\beta_{j}\), the coefficients of the geographic distance, factor endowment, cultural distance, and institutional distance were 1.0964, 0.0720, 0.2569, and 0.3241, respectively. Using Equation (9), we obtained \(f_{j}\), or the weights of the geographic distance, factor endowment distance, cultural distance, and institutional distance as 0.6187, 0.0348, 0.1523, and 0.1942, respectively. \[f_{j}=\beta_{j}/\sum_{j=1}^{4}\beta_{j}\,j=1,\,2,\,3,\,4.\] (9)
4. Computation and ranking of comprehensive distance indices. We used Equation (10) to calculate the weighted mean of the geographic distance, the factor endowment distance, the cultural distance, and the institutional distance, We used the reverse conversion method to obtain the ranking of the comprehensive distance indices between China and the Belt and Road countries (Table 4). \[y_{i}=\sum_{j=1}^{4}X_{ij}f_{j}/\sum_{j=1}^{4}f_{j}\,i=1,\,2,\ldots,62.\] (10)  
The comprehensive distance indices are not absolute distance in space. The indices only have relative meaning, so are only valuable when compared, so that the value could be negative. The countrywith potentially negative smaller comprehensive distance indices from China would have the greater potential for deep cooperation, whereas a country with larger comprehensive distance indices from China would have a smaller potential for deep cooperation.