Multi-Universality and Localized Attacks in Spatially Embedded Networks

Gross, Bnaya; Vaknin, Dana; Danziger, Michael M.; Havlin, Shlomo

doi:10.7566/jpscp.16.011002

Cited by 12 publications

(18 citation statements)

References 35 publications

(37 reference statements)

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“…We find that a nucleation phenomenon can be triggered by local damage, with failures spreading through the entire system. The cascade itself has random behavior on a small scale but spatial behavior on a large scale, similar to what has been observed in the single-layer case [48,63]. We further find that the critical nucleation size has novel scaling features.…”

Section: Discussionsupporting

confidence: 80%

“…Once the damage spreads beyond this neighborhood, it expands linearly in space, with a constant rate and a parabolic decrease in ¥ P , as documented for spatially embedded interdependent networks [31,32,35]. A similar coexistence of random and spatial properties, differentiated by scale, has been observed in the single-layer case [48,63].…”

Section: Resultsmentioning

confidence: 52%

“…Here, we study localized attacks on a realistic spatial multiplex model that has been proposed recently [47,48]. The system is a model of multiplex with exponential link-length distribution of connectivity links in each of the two layers:…”

Section: Introductionmentioning

confidence: 99%

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Spreading of localized attacks in spatial multiplex networks

2017

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Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or natural catastrophes, which affect all nodes within a given radius. Here we study the effects of localized attacks on spatial multiplex networks of two layers. We find a metastable region where a localized attack larger than a critical size induces a nucleation transition as a cascade of failures spreads throughout the system, leading to its collapse. We develop a theory to predict the critical attack size and find that it exhibits novel scaling behavior. We further find that localized attacks in these multiplex systems can induce a previously unobserved combination of random and spatial cascades. Our results demonstrate important vulnerabilities in real-world interdependent networks and show new theoretical features of spatial networks.

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Section: Discussionsupporting

confidence: 80%

Section: Resultsmentioning

confidence: 52%

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Spreading of localized attacks in spatial multiplex networks

2017

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“…The homogeneous model studied in [13,15,17,18] assumes two dimensional grid size L × L with L being the lattice length. The construction of the model consists of the following stages: (i) a single node is randomly chosen.…”

Section: Heterogeneous and Homogeneous Spatial Modelsmentioning

confidence: 99%

“…One of the most important properties of a network is its structure. The structure of a network can vary in many ways such as interplay between random to spatial structure [13][14][15][16][17][18], different degree distribution [19], clustering [20,21] or community structure [22][23][24][25] which have a significant effect on the phenomena that appear on it.…”

mentioning

confidence: 99%

Two transitions in spatial modular networks

et al. 2020

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Understanding the resilience of infrastructures, such as a transportation network, has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with characteristic link length such as power-grids and the brain. However, although many real-world networks are spatially embedded and their links have characteristics length such as pipelines, power lines or ground transportation lines they are not homogeneous but rather heterogeneous. For example, density of links within cities are significantly higher than between cities. Here we develop and study numerically and analytically a similar realistic heterogeneous spatial modular model using percolation process to better understand the effect of heterogeneity on such networks. The model assumes that inside a city there are many lines connecting different locations, while long lines between the cities are sparse and usually directly connecting only a few nearest neighbours cities in a two dimensional plane. We find that our heterogeneous model experiences two distinct continuous transitions, one when the cities disconnect from each other and the second when each city breaks apart. This is in contrast to the homogeneous model where a single transition is found. Although the critical threshold for site percolation in 2D grid remains an open question we analytically find the critical threshold for site percolation in this model. In addition, it has been found that the homogeneous model experience a single transition having a unique phenomenon called critical stretching where a geometric crossover from random to spatial structure in different scales found to stretch non-linearly with the characteristic length at criticality. In marked contrast, we show here that the heterogeneous model does not experience such a phenomenon indicating that critical stretching strongly depends on the network structure.

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Epidemic spreading and control strategies in spatial modular network

Gross

Havlin

2020

Appl Netw Sci

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Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the susceptible-infected-recovered model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels between cities are less and usually directly connect only a few nearest neighbor cities in a two-dimensional plane. We find that the model experience two epidemic transitions. The first lower threshold represents a local epidemic spread within a city but not to the entire country and the second higher threshold represents a global epidemic in the entire country. Based on our analytical solution we proposed several control strategies and how to optimize them. We also show that while control strategies can successfully control the disease, early actions are essentials to prevent the disease global spread.

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Multi-Universality and Localized Attacks in Spatially Embedded Networks

Cited by 12 publications

References 35 publications

Spreading of localized attacks in spatial multiplex networks

Spreading of localized attacks in spatial multiplex networks

Two transitions in spatial modular networks

Epidemic spreading and control strategies in spatial modular network

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