Search

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known in social science as Exponential Random Graphs, have been proposed with the aim of reproducing each of these properties in isolation. Here, we define a generalized ensemble of graphs by introducing the concept of graph temperature, controlling the degree of topological optimization of a network. We consider the temperature-dependent version of both existing and novel models and show that all the aforementioned topological properties can be simultaneously understood as the natural outcomes of an optimized, low-temperature topology. We also show that seemingly different graph models, as well as techniques used to extract information from real networks are all found to be particular low-temperature cases of the same generalized formalism. One such technique allows us to extend our approach to real weighted networks. Our results suggest that a low graph temperature might be a ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems. [ABSTRACT FROM AUTHOR]

The concepts of economic fitness and complexity, based on iterative and interdependent definitions of the quality of exporting countries and exported products, have led to novel insights into the dynamics of production and trade. A key step in the calculation of these quantities is the preliminary identification of statistically relevant country-product pairs.In this paper, we propose a method that could improve the current practice of filtering based on the revealed comparative advantage, by employing the maximum-entropy principle to construct an unbiased link weight probability distribution that, unlike the traditional thresholding method, allows for the statistical assessment of empirical trade volumes. The result is an adjusted geometric distribution for trade links that refines the revealed comparative advantage approach. This allows us to define the statistical significance of each trade link weight, leading to statistically supported trade link filtering decisions. Using this statistically justified filtering method, we have obtained results that are similar in nature to those that were found without this method, even though there are significant deviations in the details. In addition, the statistical information thus obtained on each trade link allows us to perform a spectral analysis of the export portfolio of individual economies. [ABSTRACT FROM AUTHOR]