Xuqing Huang

Robustness of interdependent networks under targeted attack

When an initial failure of nodes occurs in interdependent networks, a cascade of failure between the networks occurs. Earlier studies focused on random initial failures. Here we study the robustness of interdependent networks under targeted attack on high or low degree nodes. We introduce a general technique which maps the targeted-attack problem in interdependent networks to the random-attack problem in a transformed pair of interdependent networks. We find that when the highly connected nodes are protected and have lower probability to fail, in contrast to single scale-free (SF) networks where the percolation threshold pc = 0, coupled SF networks are significantly more vulnerable with pc significantly larger than zero. The result implies that interdependent networks are difficult to defend by strategies such as protecting the high degree nodes that have been found useful to significantly improve robustness of single networks.

Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation

As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008–2011.

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., 103 (2009) 058701), we develop an analytical method for studying how clustering within the networks of a system of interdependent networks affects the systems robustness. We find that clustering significantly increases the vulnerability of the system, which is represented by the increased value of the percolation threshold pc in interdependent networks. Copyright c EPLA, 2013

Partial correlation analysis: applications for financial markets

The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price changes for a given pair of stocks, but it does not measure whether other stocks influence the relationship between them. To explore the influence of a third stock on the relationship between two stocks, we use a partial correlation measurement to determine the underlying relationships between financial assets. Building on previous work, we present a statistically robust approach to extract the underlying relationships between stocks from four different financial markets: the United States, the United Kingdom, Japan, and India. This methodology provides new insights into financial market dynamics and uncovers implicit influences in play between stocks. To demonstrate the capabilities of this methodology, we (i) quantify the influence of different companies and, by studying market similarity across time, present new insights into market structure and market stability, and (ii) we present a practical application, which provides information on the how a company is influenced by different economic sectors, and how the sectors interact with each other. These examples demonstrate the effectiveness of this methodology in uncovering information valuable for a range of individuals, including not only investors and traders but also regulators and policy makers.

Robustness of a partially interdependent network formed of clustered networks

Clustering, or transitivity, a behavior observed in real-world networks, affects network structure and function. This property has been studied extensively, but most of this research has been limited to clustering in single networks. The effect of clustering on the robustness of coupled networks, on the other hand, has received much less attention. Only the case of a pair of fully coupled networks with clustering has recently received study. Here we generalize the study of clustering of a fully coupled pair of networks and apply it to a partially interdependent network of networks with clustering within the network components. We show, both analytically and numerically, how clustering within networks affects the percolation properties of interdependent networks, including the percolation threshold, the size of the giant component, and the critical coupling point at which the first-order phase transition changes to a second-order phase transition as the coupling between the networks is reduced. We study two types of clustering, one proposed by Newman [Phys. Rev. Lett. 103, 058701 (2009)] in which the average degree is kept constant while the clustering is changed, and the other by Hackett et al. [Phys. Rev. E 83, 056107 (2011)] in which the degree distribution is kept constant. The first type of clustering is studied both analytically and numerically, and the second is studied numerically.

Network of Interdependent Networks: Overview of Theory and Applications

Complex networks appear in almost every aspect of science and technology. Previous work in network theory has focused primarily on analyzing single networks that do not interact with other networks, despite the fact that many real-world networks interact with and depend on each other. Very recently an analytical framework for studying the percolation properties of interacting networks has been introduced. Here we review the analytical framework and the results for percolation laws for a network of networks (NON) formed by \(n\) interdependent random networks. The percolation properties of a network of networks differ greatly from those of single isolated networks. In particular, although networks with broad degree distributions, e.g., scale-free networks, are robust when analyzed as single networks, they become vulnerable in a NON. Moreover, because the constituent networks of a NON are connected by node dependencies, a NON is subject to cascading failure. When there is strong interdependent coupling between networks, the percolation transition is discontinuous (is a first-order transition), unlike the well-known continuous second-order transition in single isolated networks. We also review some possible real-world applications of NON theory.