International trade is based on a set of complex relationships between different countries that can be modelled as a dense network of interconnected agents. A long-standing problem in this field is the detection of communities, as it reveals how the network is internally organized, highlighting the presence of special relationships between nodes, that might not be revealed by direct empirical analyses.
In this framework, a specific role is assumed by the distance between nodes. In the economic field, a network perspective is based on the idea that indirect trade relationships may be important [1]. A measure of the distance between nodes that also considers indirect connections is therefore crucial to catch interconnections between nodes. In this work, we focus on two measures of distance, or metrics, on the network: the Estrada communicability distance [2] and the vibrational communicability distance [3]. They both go beyond the limits of the immediate interaction between neighbours and they look simultaneously, albeit differently, at all the possible channels of interactions between nodes. We propose a specific methodology that exploits such metrics to inspect the mesoscale structure of the network, in search for strongly interacting clusters of nodes. Using these metrics we group nodes whose mutual distances are below a given threshold, i.e. whose interactions are stronger than a given value. Then we identify the optimal partition according to a maximum quality function criterion. Unlike the classical modularity function, we adapt the partition quality index proposed in [4] for general metric spaces, exploiting the additional information of the network’s metric structure. Among all the different partitions we get at different thresholds, we select the one providing the maximum quality index, according to the criterion described in [4].
Our proposal is efficient from a computational viewpoint. Indeed, given the specific distance matrix, we can easily evaluate the optimal solution varying the threshold. We cluster nodes going beyond the interactions between neighbours and considering all possible channels of interaction between them. The approach turns out to be particularly suitable when applied to a dense network like the World Trade Network.
Numerical results depict the structure of the economic trade, detecting main relevant communities. Features and properties of each community can be exploited to compare the characteristics of different clusters and to detect the most central countries inside the single community as well in the whole network.
References
[1] G. Fagiolo, J.N. Victor, M. Lubell, A. Montgomery, The Oxford Handbook of Political Networks (2015) 173–193
[2] E. Estrada, N. Hatano, N, Appl. Math. Comput. 214(2), 500–511 (2009)
[3] E. Estrada, The structure of complex networks: theory and applications. Oxford University Press (2012)
[4] C. Chang, W. Liao, Y. Chen, L. Liou, IEEE Transactions on Network Science and Engineering 3(1), 2–16 (2016)