Interdependent lattice networks in high dimensions

Lowinger, Steven; Cwilich, Gabriel; Buldyrev, Sergey V.

doi:10.1103/physreve.94.052306

Cited by 19 publications

(36 citation statements)

References 27 publications

(39 reference statements)

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“…One can see that the larger networks becomes more vulnerable than the smaller ones. This phenomenon is similar to the one observed in [9] for high dimensional interdependent lattices. For all values of N , the curves p t (α) approach the critical point p c ≈ 0.38 from above.…”

Section: Size Dependence Of the Transition Pointsupporting

confidence: 88%

“…The principal characteristics of the first-order phase transition is the bimodality of the distribution of the order parameter, which can be either the fraction of surviving nodes or the fraction of nodes in the giant component at the end of the cascade of failures. For these first-order transitions, we can numerically find p t as the value at which the areas of both peaks, corresponding to large and small fractions of surviving nodes, are equal to each other [9]. This coincides with the value of p at which the average length of the cascade reaches a maximum.…”

Section: Numerical Results Of the Threshold Pointsupporting

confidence: 53%

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Network overload due to massive attacks

et al. 2018

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We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade p_{f} as a function of the strength of the initial attack, measured by the fraction of nodes p that survive the initial attack for different values of tolerance α in random regular and Erdös-Renyi graphs. We find the existence of a first-order phase-transition line p_{t}(α) on a p-α plane, such that if pp_{t}, p_{f} is large and the giant component of the network is still present. Exactly at p_{t}, the function p_{f}(p) undergoes a first-order discontinuity. We find that the line p_{t}(α) ends at a critical point (p_{c},α_{c}), in which the cascading failures are replaced by a second-order percolation transition. We find analytically the average betweenness of nodes with different degrees before and after the initial attack, we investigate their roles in the cascading failures, and we find a lower bound for p_{t}(α). We also study the difference between localized and random attacks.

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Section: Size Dependence Of the Transition Pointsupporting

confidence: 88%

Section: Numerical Results Of the Threshold Pointsupporting

confidence: 53%

Network overload due to massive attacks

et al. 2018

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“…The percolation theory is one of the simplest models in probability theory, which has been applied to a wide range of phenomena in physics, chemistry, biology, and materials science where connectivity and clustering play an important role: flow in porous materials [1][2][3], network theory [4][5][6][7][8][9], thermal phase transitions [10,11], spread of the computer virus [12], transport in disordered media [13,14], electrical conductivity in alloys [15][16][17][18], simulated spread fire in multi-compartmented structures [19] and the spread of epidemics [20]. Percolation theory has also provided insight into the behavior of more complicated models exhibiting phase transitions and critical phenomena [1,2,[21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…Percolation theory can also be used to understand network robustness, i.e., how the structure of a network changes as its elements (sites/bonds) are removed either through random or malicious attacks [4][5][6][7][8][9]. The focus of robustness in complex networks is the response of the network to the removal of nodes or links.…”

Section: Introductionmentioning

confidence: 99%

Percolation phase transition by removal ofk2-mers from fully occupied lattices

2019

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Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of k × k square tiles (k 2-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then, the system is diluted by removing k 2-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, p c,k , for which the connectivity disappears. This particular value of the concentration is called inverse percolation threshold, and determines a well-defined geometrical phase transition in the system. The results obtained for p c,k show that the inverse percolation threshold is a decreasing function of k in the range 1 ≤ k ≤ 4. For k ≥ 5, all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent νj was measured, being νj = 1 regardless of the size k considered. In addition, the accurate determination of the critical exponents ν, β and γ reveals that the percolation phase transition involved in the system, which occurs for k varying between 1 and 4, has the same universality class as the standard percolation problem.

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“…[73] is present only below 6 dimensions, suggesting that as in regular percolation, 6 is the upper critical dimension of this problem. Later works expand these studies to randomly connected graphs [68] in which the length of the dependency links is defined as a chemical distance, and to high dimensional lattices [77]. Similar model [13,121] with diluted lattices and dependency links of length r = 0 also produces a continuous transition as the model of Ref.…”

Section: Spatial Interdependent Networkmentioning

confidence: 98%

Cascading failures in complex networks

Valdez

Shekhtman

Rocca

et al. 2020

Journal of Complex Networks

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Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behaviour. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.

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Interdependent lattice networks in high dimensions

Cited by 19 publications

References 27 publications

Network overload due to massive attacks

Network overload due to massive attacks

Percolation phase transition by removal ofk2-mers from fully occupied lattices

Cascading failures in complex networks

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