Clusters in weighted macroeconomic networks : the EU case. Introducing the overlapping index of GDP/capita fluctuation correlations

GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990-2005. The target group of countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and evolution of the EU country clusters in a macroeconomic sense.

💡 Research Summary

The paper investigates the co‑movement of per‑capita Gross Domestic Product (GDP) among the 25 European Union (EU) member states over the period 1990‑2005. The authors first divide the whole observation window into a series of equal‑length time windows (TW). Within each window they compute the Pearson correlation coefficient r_{ij}^{(k)} for every pair of countries i and j, where k indexes the window. The mean correlation across all windows, (\bar r_{ij}), is then taken as the weight w_{ij} of the link connecting i and j in a fully‑connected weighted network. Positive weights indicate synchronous GDP fluctuations, negative weights indicate opposite‑direction movements.

A novel metric, the overlapping index O_i, is introduced to quantify how strongly a node i is embedded in the overall network. O_i is defined as the normalized average of the absolute weights of all links incident to i:

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