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Revealing the community structure exhibited by real networks is a fundamental phase towards a comprehensive understanding of complex systems beyond the local organization of their components. Community detection techniques help on providing insights into understanding the local organization of the components of networks. In this study we identify and investigate the overlapping community structure of an interesting and unique case of study: the Estonian network of payments. In order to perform the study, we use the Clique Percolation Method and explore statistical distribution functions of the communities, where in most cases we found scale-free properties. In this network the nodes represent Estonian companies and the links represent payments done between the companies. Our study adds to the literature of complex networks by presenting the first overlapping community detection analysis of a country's network of payments., pre-print

This work uses wavelets in determining Hurst´s coefficient of the most important stock indices of four emerging markets known as the next new economies that will compound the BRIC group: Mexico, North Korea, Turkey and Indonesia. The objectives are: to determine whether or not persistence behavior in the long run exists for these indices; if under this perspective they should be considered as emerging markets or mature markets, to assess the non-linear and fractal characteristics (if found), to verify if it is possible to estimate future tendencies using wavelet techniques, to assess the results and to find new possibilities for financial fractal analysis and to seek other alternatives under this investigation research line. Finally, this work proposes a research field more viable and in accordance with the criticism to random walk and EMH (Efficient Market Hypothesis) approach of markets

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank, hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks., Comment: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, 2016