Existence and significance of communities in the World Trade Web

The World Trade Web (WTW), which models the international transactions among countries, is a fundamental tool for studying the economics of trade flows, their evolution over time, and their implications for a number of phenomena, including the propagation of economic shocks among countries. In this respect, the possible existence of communities is a key point, because it would imply that countries are organized in groups of preferential partners. In this paper, we use four approaches to analyze communities in the WTW between 1962 and 2008, based, respectively, on modularity optimization, cluster analysis, stability functions, and persistence probabilities. Overall, the four methods agree in finding no evidence of significant partitions. A few weak communities emerge from the analysis, but they do not represent secluded groups of countries, as intercommunity linkages are also strong, supporting the view of a truly globalized trading system.

Figure 1

The (normalized) modularity $Q\left(V\right)$ of the perturbed partitions obtained, from the optimal one [$Q\left(0\right)=Q_{\max }$], by relabeling 10$\%$ to 50$\%$ of the nodes, i.e., by assigning them to a different community. $V$ is the variation of information of the perturbed partitions. The (blue) curve with filled circles was obtained by relabeling randomly selected nodes (each point is the average of 100 realizations); the (red) curve with filled triangles is obtained by relabeling the least connected nodes (lowest strength or degree).

Figure 2

Dendrograms obtained by hierarchical cluster analysis. From top to bottom: WTW in 1962, 1980, and 2008; GN benchmark network; and LFR benchmark network. Colors (other than black) denote groups of nodes whose distances are all not larger than $0.7$.

Figure 3

Top: Stability functions $r_t^H$ of the GN and LFR benchmark networks and those of the World Trade Web (WTW) in 1962, 1980, and 2008. For each network, we consider the partition $H$ obtained via modularity optimization. Bottom: Same as above, but the stability is normalized by the initial value $r_1^H$ and the time axis is normalized, separately for each curve, by the number $N$ of network nodes.

Figure 4

Persistence probabilities of the World Trade Web (WTW; 1962–2008) and of the GN and LFR benchmark networks. The three panels refer, respectively, to the original, filtered, and symmetrized WTW, as defined in Sec. 3a. For each network, we consider the $q$-community partition obtained via modularity optimization: the $q$ horizontal dashes denote the values of the diagonal terms $u_{cc}$ of the lumped Markov matrix $U$ (vertical straight lines are for visual aid only).