Cluster Expansion Method for Evolving Weighted Networks Having Vector-Like Nodes

Abstract

The cluster variation method known in statistical mechanics and condensed matter is revived for weighted bipartite networks. The decomposition (or expansion) of a Hamiltonian through a finite number of components, whence serving to define variable clusters, is recalled. As an illustration the network built from data representing correlations between (4) macroeconomic features, i.e. the so-called vector components, of 15 EU countries, as (function) nodes, is discussed. We show that statistical physics principles, like the maximum entropy criterion points to clusters, here in a (4) variable phase space: Gross Domestic Product, Final Consumption Expenditure, Gross Capital Formation and Net Exports. It is observed that the maximum entropy corresponds to a cluster which does not explicitly include the Gross Domestic Product but only the other (3) "axes", i.e. consumption, investment and trade components. On the other hand, the minimal entropy clustering scheme is obtained from a coupling necessarily including Gross Domestic Product and Final Consumption Expenditure. The results confirm intuitive economic theory and practice expectations at least as regards geographical connexions. The technique can of course be applied to many other cases in the physics of socio-economy networks.

Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices

“…Thus, further work, if we may suggest so, should be programed to apply the approach in view of obtaining results on disordered systems characterized, e.g., (i) by symmetric matrices having more complicated structures, as in financial or socio-economic matters [55][56][57], or (ii) when more than one type of disorder appears, as is the case very often in materials [58][59][60], and (iii) by nonsymmetric matrices: see the cases of citation or co-authorship networks implying link ordering [61][62][63], that of bipartite graphs [64], that of physiology [65], or that of financial markets [66][67][68][69][70], among recent relevant cases.…”

Inferring cultural regions from correlation networks of given baby names

“…Nowadays, many topics are based on network models, spanning biological, ecological, and economic systems as well as cultural systems [16,17,18,19,20,21,22]. Most of these are best described by weighted networks.…”

Organization of networks with tagged nodes and biased links: A priori distinct communities

“…being a so called ''ordinal'' or continuous-like variable attached at a node [62]. The final step could be to develop a Hamiltonian method, through some time-dependent Hamiltonian, as in macroeconomic studies [63,64].…”