Percolation theory on interdependent networks based on epidemic spreading

Son, Seung‐Woo; Bizhani, Golnoosh; Christensen, Claire; Grassberger, Peter; Paczuski, Maya

doi:10.1209/0295-5075/97/16006

Cited by 287 publications

(342 citation statements)

References 17 publications

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“…This algorithm has been first proposed by Son et al [13]. According to this algorithm, nodes send messages along their links to neighbor nodes.…”

Section: A the Message Passing Algorithmmentioning

confidence: 99%

“…These methods are versatile, as they can be applied not only to ensembles of random networks, but also to single network realizations. For these reasons these algorithms are becoming increasingly popular in network science with applications ranging from percolation on single and multilayer networks to controllability [13,15,[34][35][36]43,47]. These algorithms proceed by iteration of dynamical rules, which determine messages or beliefs that a node sent to a neighboring node.…”

Section: A General Observations On the Message Passing Algorithm Formentioning

confidence: 99%

“…The interdependence between nodes implies that a node is damaged if its interdependent nodes are damaged. Recently, a generalized percolation process has been proposed to study the robustness of multilayer networks in the presence of interdependencies [11][12][13]. This model allows us to understand and to control the fragility of interconnected infrastructures.…”

Section: Introductionmentioning

confidence: 99%

“…A generalization of the giant connected component for multilayer networks with interdependencies between the nodes is called a mutually connected giant component (MCGC) [11][12][13]. As the fraction of damaged nodes increases, a discontinuous, hybrid phase transition occurs, after which the MCGS emerges, and the response of the system to perturbation is characterized by large avalanches of failure events that propagate back and forth between different layers [11].…”

Section: Introductionmentioning

confidence: 99%

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Message passing theory for percolation models on multiplex networks with link overlap

2016

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Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers M. Specifically we propose and compare two message passing algorithms that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has nontrivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

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“…This algorithm has been first proposed by Son et al [13]. According to this algorithm, nodes send messages along their links to neighbor nodes.…”

Section: A the Message Passing Algorithmmentioning

confidence: 99%

Section: A General Observations On the Message Passing Algorithm Formentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Message passing theory for percolation models on multiplex networks with link overlap

2016

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“…This is a set of nodes identified in a recursive manner, and composed of vertices that are simultaneously in the largest clusters of both network layers thanks only to connections with other nodes within the set. 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].…”

mentioning

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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Leveraging Network Theory and Stress Tests to Assess Interdependencies in Critical Infrastructures

Galbusera

Giannopoulos

2019

Advanced Sciences and Technologies for Security Applications

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Percolation theory on interdependent networks based on epidemic spreading

Cited by 287 publications

References 17 publications

Message passing theory for percolation models on multiplex networks with link overlap

Message passing theory for percolation models on multiplex networks with link overlap

Percolation in real interdependent networks

Leveraging Network Theory and Stress Tests to Assess Interdependencies in Critical Infrastructures

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