Avoiding catastrophic failure in correlated networks of networks

Reis, Saulo D. S.; Hu, Yanqing; Babino, Andrés; Andrade, José S.; Canals, Santiago; Sigman, Mariano; Makse, Hernán A.

doi:10.1038/nphys3081

Cited by 242 publications

(244 citation statements)

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“…In some real-world networks, the indegree k in and out-degree k out of a given node are correlated with the form k out ∝ k α in (32,33). The correlation between in-degree and out-degree is positive, negative, or not correlated when the coefficient α ∈ ð0,1 , α ∈ ½−1,0Þ and α = 0, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Ref. 32 shows that the stability of a system relies on the in-degree and out-degree correlations between the coupled nodes in interdependent networks because these correlations curtail the tendency to catastrophic failure caused by the Significance Real-world complex systems interact with one another, and these interactions increase the probability of catastrophic failure. Using interdependent networks to model these phenomena helps understand a system's robustness and enables design of more robust infrastructures.…”

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confidence: 99%

“…We develop here a theoretical framework for analyzing the breakdown of interdependent directed networks with and without in-degree k in and out-degree k out correlations, measured by a coefficient α with the form k out ∝ k α in (32,33), and we apply it to real interdependent international trade networks. Our analysis leads to several unexpected results:…”

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confidence: 99%

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Breakdown of interdependent directed networks

Liu

Stanley

Gao

2016

Proc. Natl. Acad. Sci. U.S.A.

142

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Increasing evidence shows that real-world systems interact with one another via dependency connectivities. Failing connectivities are the mechanism behind the breakdown of interacting complex systems, e.g., blackouts caused by the interdependence of power grids and communication networks. Previous research analyzing the robustness of interdependent networks has been limited to undirected networks. However, most real-world networks are directed, their in-degrees and out-degrees may be correlated, and they are often coupled to one another as interdependent directed networks. To understand the breakdown and robustness of interdependent directed networks, we develop a theoretical framework based on generating functions and percolation theory. We find that for interdependent Erd} os-Rényi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions. We also find that the percolation behavior of interdependent directed scale-free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness: the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correlations, confirming our theoretical analysis.interdependent networks | directed networks | degree correlations | percolation theory

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

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Breakdown of interdependent directed networks

Liu

Stanley

Gao

2016

Proc. Natl. Acad. Sci. U.S.A.

142

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“…It has been proved that, in infinitely large interconnected systems composed of two uncorrelated random networks, the percolation transition, monitored through the size of the largest cluster of mutually connected nodes, is discontinuous [10,14,15]. This result has been however shown to not apply to more general network models that account for degree correlations [16,17]. Unfortunately, all these theoretical approaches have been developed under two special, and unrealistic, assumptions.…”

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confidence: 99%

Percolation in real interdependent networks

2015

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The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network layers has been extensively studied in recent years. However, the theoretical frameworks developed so far apply only to special models in the limit of infinite sizes. These methods are therefore of little help in practical contexts, given that real interconnected networks have finite size and their structures are generally not compatible with those of graph toy models. Here, we introduce a theoretical method that takes as inputs the adjacency matrices of the layers to draw the entire phase diagram for the interconnected network, without the need of actually simulating any percolation process. We demonstrate that percolation transitions in arbitrary interdependent networks can be understood by decomposing these system into uncoupled graphs: the intersection among the layers, and the remainders of the layers. When the intersection dominates the remainders, an interconnected network undergoes a continuous percolation transition. Conversely, if the intersection is dominated by the contribution of the remainders, the transition becomes abrupt even in systems of finite size. We provide examples of real systems that have developed interdependent networks sharing a core of "high quality" edges to prevent catastrophic failures.Percolation is among the most studied topics in statistical physics [1]. The model used to mimic percolation processes assumes the existence of an underlying network of arbitrary structure. Regular grids are traditionally considered to model percolation in materials [2,3]. Complex graphs are instead assumed as underlying supports in the analysis of spreading phenomena in social environments [4,5], or in robustness studies of technological and infrastructural systems [6][7][8]. Once the network has been specified, a configuration of the percolation model is generated assuming nodes (or sites) present with probability p. For p = 0, only a disconnected configuration is possible. For p = 1 instead, all nodes are within the same connected cluster. As the occupation probability varies, the network undergoes a structural transition between these two extreme configurations. Although there are special substrates, e.g., one-dimensional lattices, where the percolation transition may be discontinuous, in the majority of the cases, random percolation models give rise to continuous structural changes [9]. This means that the size of the largest cluster in the network, used as a proxy for the connectedness of the system, increases from the non-percolating to the percolating phases in a smooth fashion.The percolation transition may become discontinuous in a slightly different model involving not just a single network, but a system composed of two or more interdependent graphs [10]. This is a very realistic scenario considering that many, if not all, real graphs are "coupled" with ...

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“…This generalized percolation transition has been studied on multiplex networks, multilayer network and network of networks finding a rich phenomenology [72,[75][76][77][78][79][80][81]. Multilayer networks found in biological systems [20], are different from man-made multilayer infrastructures, and they display a significant robustness allowing them to survive biological selection. Characterizing them could contribute to a better design of complex infrastructures.…”

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confidence: 99%

Interdisciplinary and physics challenges of network theory

Bianconi¹

2015

EPL

136

148

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-Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.Introduction. -Network theory has emerged almost twenty years ago, as a new field for characterizing interacting complex systems, such as the Internet, the biological networks of the cell, and social networks. It is now time to reflect on the maturity of the field, indicating the main results obtained so far and the big challenges that lie ahead.Initially, the physics perspective, in particular the statistical mechanics approach, has dominated the field of Network Theory [1][2][3][4][5][6][7]. This point of view has played a central role to characterize the universal properties of the structure of complex networks. It has been found that despite the diversity of complex networks, ranging from the Internet to the protein interaction networks in the cell, most networks obey universal properties: they are small-world [9], they are scale-free [8], and they have a non trivial community structure [7]. Moreover, over the years, special attention has been addressed to the interplay between network structure and dynamics [10,11]. In fact phase diagrams of critical phenomena and dynamical processes change drastically when the dynamics is defined on complex networks. Complex networks are responsible for significant changes in the critical behaviour of percolation, Ising model, random walks, epidemic spreading, synchronization, and controllability of networks [10][11][12][13].The need to characterize complex systems, to extract relevant information from them, and to understand how dynamical processes are affected by network structure, has never been more severe than in the XXI century when we are witnessing a Big Data explosion in social sciences, information and communication technologies and in biology.

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Avoiding catastrophic failure in correlated networks of networks

Cited by 242 publications

References 29 publications

Breakdown of interdependent directed networks

Breakdown of interdependent directed networks

Percolation in real interdependent networks

Interdisciplinary and physics challenges of network theory

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