Journal Article•
Catastrophic cascade of failures in interdependent networks
TL;DR: This work develops a framework for understanding the robustness of interacting networks subject to cascading failures and presents exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks.
Abstract: Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures (‘concurrent malfunction’) is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.
Citations
More filters
[...]
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.
7,116 citations
Posted Content•
TL;DR: In this paper, a cascading failure model was proposed to describe the risk propagation process during crises and 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.
Abstract: 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.
169 citations
Posted Content•
TL;DR: A unique database of supervisory reports of Italian banks to the Banca d'Italia is employed that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract to find that layers have different topological properties and persistence over time.
Abstract: The interbank market has a natural multiplex network representation. We employ a unique database of supervisory reports of Italian banks to the Banca d'Italia that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract. We find that layers have different topological properties and persistence over time. The presence of a link in a layer is not a good predictor of the presence of the same link in other layers. Maximum entropy models reveal different unexpected substructures, such as network motifs, in different layers. Using the total interbank network or focusing on a specific layer as representative of the other layers provides a poor representation of interlinkages in the interbank market and could lead to biased estimation of systemic risk.
149 citations
Cites background from "Catastrophic cascade of failures in..."
...Buldyrev et al. (2010) find that interdependent networks become significantly more vulnerable to contagion compared to their non-interacting sub-networks....
[...]
Journal Article•
TL;DR: In this article, the authors propose to reduce the interconnected networks to a set of decoupled graphs, which provides a route to probing finite sizes, and they show that decoupling networks can be used to study how catastrophe propagates in multi-layered networks.
Abstract: Our understanding of how catastrophe propagates in multi-layered networks relies on theories that apply only to infinite systems. Reducing the interconnected networks to a set of decoupled graphs provides a route to probing finite sizes.
148 citations
Journal Article•
TL;DR: In this paper, the authors show that market integration and diversification can contribute to creating cyclical structures which tend to amplify financial distress, thereby undermining systemic stability and making large crises more likely.
Abstract: Following the financial crisis of 2007–2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily distress can spread within the system. However, in financial network models, the details of how financial institutions interact typically play a decisive role, and a general understanding of precisely how network topology creates instability remains lacking. Here we show how processes that are widely believed to stabilize the financial system, that is, market integration and diversification, can actually drive it towards instability, as they contribute to create cyclical structures which tend to amplify financial distress, thereby undermining systemic stability and making large crises more likely. This result holds irrespective of the details of how institutions interact, showing that policy-relevant analysis of the factors affecting financial stability can be carried out while abstracting away from such details.
141 citations
References
More filters
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
39,297 citations
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
"Catastrophic cascade of failures in..." refers background in this paper
...f the entire graph. While in the BA network, the preferential attachment rule develops correlations in the network and a scale-free degree distribution is obtained, which in a general way is given by [24], P(k) = ˆ ck−γ m ≤k < K 0 otherwise (2) , where γ is the degree exponent and K an upper limit due to the system finite size. The power-law degree distribution favors the existence of highly connect...
[...]
... and critical properties can be found elsewhere [5, 6]. In this article we focus on two types of model networks: a random graph (Erd˝os-R´enyi) [21, 22, 23] and a scale-free network (Barab´asiAlbert) [24]. The Erdo˝s-R´enyi (ER) network is a random graph obtained by randomly distributing M links between N nodes, being a statistical ensemble with equal probability for any generated configuration. The sc...
[...]
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them.
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other.
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
18,415 citations
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
17,647 citations
"Catastrophic cascade of failures in..." refers background in this paper
...The last decade witnessed an intensive study of complex networks [1, 2, 3, 4, 5, 6] boosted by several real-world data revealing complex structures in the topology of their network like, Internet, airport connections, and power grids [7]....
[...]
Book•
25 Mar 2010
TL;DR: This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Abstract: The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.
10,567 citations
"Catastrophic cascade of failures in..." refers background in this paper
...from those of single-network systems. In this article, these results are reviewed and the main properties discussed. 1. – Introduction The last decade witnessed an intensive study of complex networks [1, 2, 3, 4, 5, 6] boosted by several real-world data revealing complex structures in the topology of their network like, Internet, airport connections, and power grids [7]. Recently, special emphasis has been focused ...
[...]