# Cluster Expansion Method for Evolving Weighted Networks Having Vector-like Nodes - Physics > Physics and Society

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Abstract: The Cluster Variation Method known in statistical mechanics and condensedmatter is revived for weighted bipartite networks. The decomposition of aHamiltonian through a finite number of components, whence serving to definevariable clusters, is recalled. As an illustration the network built from datarepresenting correlations between 4 macro-economic features, i.e. the socalled $vector$ $components$, of 15 EU countries, as function nodes, isdiscussed. We show that statistical physics principles, like the maximumentropy criterion points to clusters, here in a 4 variable phase space: GrossDomestic Product GDP, Final Consumption Expenditure FCE, Gross CapitalFormation GCF and Net Exports NEX. It is observed that the $maximum$entropy corresponds to a cluster which does $not$ explicitly include the GDPbut only the other 3 -axes-, i.e. consumption, investment and tradecomponents. On the other hand, the $minimal$ entropy clustering scheme isobtained from a coupling necessarily including GDP and FCE. The results confirmintuitive economic theory and practice expectations at least as regardsgeographical connexions. The technique can of course be applied to many othercases in the physics of socio-economy networks.

Author: ** Marcel Ausloos, Mircea Gligor**

Source: https://arxiv.org/