Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications
The G7 countries (France, USA, United Kingdom, Germany, Japan, Italy, Canada) are the most developed countries in the world, but such statement leaves unanswered the question on which of those is the most important one and of course what kind of dependencies exists between them. Of course this subject has been considered along various lines of analysis (Frankel 2000), which usually require a detailed knowledge of the analysed objects and therefore are difficult to pursue. Our own question is to investigate the dependence and leadership problem on a very limited number of data. Within this paper correlations between G7 countries, are investigated on the basis of their Gross Domestic Product (GDP). GDP is one of the most important parameters describing state of an economy and is extensively studied (Lee et al. 1998, Ormerod 2004). The annual GDP records, considered as a discrete time series are used over the last 53 years (since 1950 till 2003) in order to evaluate GDP increments and distances between those countries. Different distance functions are used and the results compared. Distance matrices are calculated in the case of discrete Hilbert spaces Lq (q = 1, 2), Eq. (1), a statistical correlation distance, Eq. (2), and a difference between increment distributions, Eq. (4). The distance functions were chosen here below taking into account considerations on basic properties of the data. The distance matrices are then analysed using graph methods in the form of a unidirectional or bidirectional chain (UMLP and BMLP respectively) (Ausloos and Miskiewicz 2005) as well as through the locally minimal spanning distance tree (LMST).