Intensive and extensive biases in economic networks: reconstructing world trade

In economic and financial networks, the strength (total value of the connections) of a given node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown. However, several studies have proved that real economic networks are topologically very different from networks inferred only from node strengths. Here we provide a detailed analysis for the World Trade Web (WTW) by comparing it to an enhanced null model that simultaneously reproduces the strength and the number of connections of each node. We study several temporal snapshots and different aggregation levels (commodity classes) of the WTW and systematically find that the observed properties are extremely well reproduced by our model. This allows us to introduce the concept of extensive and intensive bias, defined as a measurable tendency of the network to prefer either the formation of new links or the reinforcement of existing ones. We discuss the possible economic interpretation in terms of trade margins.