Assortativity Decreases the Robustness of Interdependent Networks

It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an abrupt percolation transition as failures accumulate. 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 two interdependent networks significantly changes the critical density of failures that triggers the total disruption of the two-network system. Specifically, we find that the assortativity (i.e. the likelihood of nodes with similar degree to be connected) within a single network decreases the robustness of the entire system. The results of this study on the influence of assortativity may provide insights into ways of improving the robustness of network architecture, and thus enhances the level of protection of critical infrastructures

Interdependent networks - topological percolation research and application in finance

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

The robustness of interdependent clustered networks

It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)], we develop an analytical method for studying how clustering within the networks of a system of interdependent networks affects the system's robustness. We find that clustering significantly increases the vulnerability of the system, which is represented by the increased value of the percolation threshold $p_c$ in interdependent networks.Comment: 6 pages, 6 figure

Cascading failures in coupled networks with both inner-dependency and inter-dependency links

We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We find that when most of dependency links are inner- or inter-ones, the coupled networks system is fragile and makes a discontinuous percolation transition. However, when the numbers of two types of dependency links are close to each other, the system is robust and makes a continuous percolation transition. This indicates that the high density of dependency links could not always lead to a discontinuous percolation transition as the previous studies. More interestingly, although the robustness of the system can be optimized by adjusting the ratio of the two types of dependency links, there exists a critical average degree of the networks for coupled random networks, below which the crossover of the two types of percolation transitions disappears, and the system will always demonstrate a discontinuous percolation transition. We also develop an approach to analyze this model, which is agreement with the simulation results well.Comment: 9 pages, 4 figure

Spatially self-organized resilient networks by a distributed cooperative mechanism

The robustness of connectivity and the efficiency of paths are incompatible in many real networks. We propose a self-organization mechanism for incrementally generating onion-like networks with positive degree-degree correlations whose robustness is nearly optimal. As a spatial extension of the generation model based on cooperative copying and adding shortcut, we show that the growing networks become more robust and efficient through enhancing the onion-like topological structure on a space. The reasonable constraint for locating nodes on the perimeter in typical surface growth as a self-propagation does not affect these properties of the tolerance and the path length. Moreover, the robustness can be recovered in the random growth damaged by insistent sequential attacks even without any remedial measures.Comment: 34 pages, 12 figures, 2 table