Table 1 Calculation and implications of trade network indicators.
From: Global agricultural trade network characteristics and its influencing factors
Indicator | Formula | Implication | Practical Significance |
|---|---|---|---|
Indegree, Outdegree | \({K}_{i}^{in}={\sum }_{i}^{n}{a}_{ji}\), \({K}_{i}^{out}={\sum }_{i}^{n}{a}_{ij}\) | number of directly connected nodes in a directed network | reflect the number of direct trading partner countries for imports and exports |
Harmonic closeness centrality | \(H(i)=\frac{{\sum }_{ij}\frac{1}{{d}_{ij}}}{n-1}\) | the harmonic mean of the sum of the reciprocals of the shortest path lengths from a node to all other nodes | reflect the efficiency and convenience of trade transmission |
Betweenness centrality | \(B(i)={\sum }_{j\ne k\ne i}\frac{\sigma (j,k|i)}{\sigma (j,k)}\) | the degree to which a node lies on the shortest paths of other nodes | the extent to which a country acts as an “intermediary” |
Network density | \(D=\frac{r}{n(n-1)}\) | the ratio of the number of actual edges to the maximum possible number of edges | the extent of trade connections between countries |
Average cluster coefficient | \(C=\frac{1}{n}\mathop{\sum }\limits_{i=1}^{n}\frac{2{M}_{i}}{{k}_{i}({k}_{i}-1)}\) | describe the degree of node clustering in the network | reflect the clustering trend between countries |
Average path length | \(L=\frac{1}{n(n-1)}{\sum }_{ij}{d}_{ij}\) | the average number of edges required to traverse in the trade network | reflect the efficiency of trade diversion |
Transitivity | \(T=\frac{3\times {T}_{trans}}{3\times {T}_{trans}+{T}_{open}}\) | the proportion of triangular relationships in the network | reflect the extent to which countries become triangular trade partners |
Reciprocity | \(R=\frac{p}{n}\) | the ratio of the number of reciprocal edges to the total number of edges | reflect the degree of interdependence and trade reciprocity among countries |
Community division | \(Q=\frac{1}{2m}{\sum }_{ij}\left[{A}_{ij}-\frac{{k}_{i}{k}_{j}}{2m}\right]\delta ({c}_{i},{c}_{j})\) | divide closely connected nodes into a single community | countries within the same community are more closely connected |
