Structural resilience of spatial networks with inter-links behaving as an external field

Fan, Jingfang; Dong, Gaogao; Shekhtman, Louis; Zhou, Dong; Meng, Jun; Chen, Xiaosong

doi:10.1088/1367-2630/aadceb

Cited by 17 publications

(10 citation statements)

References 26 publications

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“…Hence, the system of three exponents \beta , \delta and \gamma has two degrees of freedom in G2-core percolation. This phenomenon echoes a recent discovery for giant component based metric in modular network resilience [8,10] for continuous phase transitions. As a comparison, we show in Figure 6 the estimates of \beta = 0.07, \delta = 87, and \gamma = 0.08 for G3-core percolation, which apparently do not satisfy the Widom identity.…”

Section: Qip (Qi)supporting

confidence: 80%

“…This is similar to the paradigm established in [1,20]; however, the introduction of community structure requires a nontrivial refined treatment of the probability partition to derive solvable self-consistency equations. It is tempting to consider a version of multivariate generating functions that have been used to deal with component based resilience in modular networks [30,8,10,33]. However, we find it cumbersome with a monolithic multivariate version and choose to track the interconnections separately from intraconnections in Gk-core percolation.…”

Section: Generating Function Formalismmentioning

confidence: 99%

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Generalized K-Core Percolation in Networks with Community Structure

Shang¹

2020

SIAM J. Appl. Math.

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Community structure underpins many complex networked systems and plays a vital role when components in some modules of the network come under attack or failure. Here, we study the generalized k-core (Gk-core) percolation over a modular random network model. Unlike the archetypal giant component based quantities, Gk-core can be viewed as a resilience metric tailored to gauge the network robustness subject to spreading virus or epidemics paralyzing weak nodes, i.e., nodes of degree less than k, and their nearest neighbors. We develop two complementary frameworks, namely, the generating function formalism and the rate equation approach, to characterize the Gkcore of modular networks. Through extensive numerical calculations and simulations, it is found that G2-core percolation undergoes a continuous phase transition while Gk-core percolation for k \geq 3 displays a first-order phase transition for any fraction of interconnecting nodes. The influence of interconnecting nodes tends to be more visible nearer the percolation threshold. We find by studying modular networks with two Erd\H os--R\' enyi modules that the interconnections between modules affect the G2-core percolation phase transition in a way similar to an external field in a spin system, where Widom's identity regulating the critical exponents of the system is fulfilled. However, this analogy does not seem to exist for Gk-core with k \geq 3 in general.

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Section: Qip (Qi)supporting

confidence: 80%

Section: Generating Function Formalismmentioning

confidence: 99%

Generalized K-Core Percolation in Networks with Community Structure

Shang¹

2020

SIAM J. Appl. Math.

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“…According to the obtained results, stronger topological interdependence, in terms of either more dependency links (in full/partial interdependence) or lower tolerance (in tolerated interdependence) decreases the robustness of the multilayer network [31][32][37][38]42,[46][47]55,57]. In this regard, Fan et al [58] found the optimal fraction of interdependent nodes as r = 0.1. It suggests that if 10% of nodes have dependency links, the network is the most robust to random attacks.…”

Section: The Effect Of Topological/functional/dynamical Propertiesmentioning

confidence: 98%

Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review

2021

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Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the robustness of infrastructure systems to resist disturbances is critical for the durable performance of modern societies. Multilayer networks have been used to model the multiplicity and interrelation of infrastructure systems and percolation theory is the most common approach to quantify the robustness of such networks. This survey systematically reviews literature published between 2010 and 2021, on applying percolation theory to assess the robustness of infrastructure systems modeled as multilayer networks. We discussed all network properties applied to build infrastructure models. Among all properties, interdependency strength and communities were the most common network property whilst very few studies considered realistic attributes of infrastructure systems such as directed links and feedback conditions. The review highlights that the properties produced approximately similar model outcomes, in terms of detecting improvement or deterioration in the robustness of multilayer infrastructure networks, with few exceptions. Most of the studies focused on highly simplified synthetic models rather than models built by real datasets. Thus, this review suggests analyzing multiple properties in a single model to assess whether they boost or weaken the impact of each other. In addition, the effect size of different properties on the robustness of infrastructure systems should be quantified. It can support the design and planning of robust infrastructure systems by arranging and prioritizing the most effective properties.

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“…Crucially, the size of the perturbation that a dynamical system on a network can tolerate, which is an operational definition of the network resilience [3], depends on the structure of the network. For example, a change in the network structure induced by the removal of a fraction of nodes and the associated edges may decrease the resilience of the system [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Accuracy of a one-dimensional reduction of dynamical systems on networks

Kundu,

Kori,

Masuda

2021

Preprint

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Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature, 530, 307 (2016)] proposed a theoretical framework to reduce dynamical systems on networks, which are high-dimensional in general, to one-dimensional dynamical systems.The accuracy of this one-dimensional reduction relies on several assumptions in addition to that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation.We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the onedimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.

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Structural resilience of spatial networks with inter-links behaving as an external field

Cited by 17 publications

References 26 publications

Generalized K-Core Percolation in Networks with Community Structure

Generalized K-Core Percolation in Networks with Community Structure

Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review

Accuracy of a one-dimensional reduction of dynamical systems on networks

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