Interdependent networks - topological percolation research and application in finance
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This dissertation covers the two major parts of my Ph.D. research: i) developing a theoretical framework of complex networks and applying simulation and numerical methods to study the robustness of the network system, and ii) applying statistical physics concepts and methods to quantitatively analyze complex systems and applying the theoretical framework to study real-world systems. In part I, we focus on developing theories of interdependent networks as well as building computer simulation models, which includes three parts: 1) We report on the effects of topology on failure propagation for a model system consisting of two interdependent networks. We find that the internal node correlations in each of the networks significantly changes the critical density of failures, which can trigger the total disruption of the two-network system. Specifically, we find that the assortativity within a single network decreases the robustness of the entire system. 2) We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-p fraction of nodes. We find that as the coupling strength q between the two networks reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths q1 and q2 , which separate the behaviors of the giant component as a function of p into three different regions, and for q2 < q < q1 , we observe a hybrid order phase transition phenomenon. 3) We study the robustness of n interdependent networks with partially support-dependent relationship both analytically and numerically. We study a starlike network of n Erdos-Renyi (ER), SF networks and a looplike network of n ER networks, and we find for starlike networks, their phase transition regions change with n, but for looplike networks the phase regions change with average degree k . In part II, we apply concepts and methods developed in statistical physics to study economic systems. We analyze stock market indices and foreign exchange daily returns for 60 countries over the period of 1999-2012. We build a multi-layer network model based on different correlation measures, and introduce a dynamic network model to simulate and analyze the initializing and spreading of financial crisis. Using different computational approaches and econometric tests, we find atypical behavior of the cross correlations and community formations in the financial networks that we study during the financial crisis of 2008. For example, the overall correlation of stock market increases during crisis while the correlation between stock market and foreign exchange market decreases. The dramatic increase in correlations between a specific nation and other nations may indicate that this nation could trigger a global financial crisis. Specifically, core countries that have higher correlations with other countries and larger Gross Domestic Product (GDP) values spread financial crisis quite effectively, yet some countries with small GDPs like Greece and Cyprus are also effective in propagating systemic risk and spreading global financial crisis.