Critical Stretching of Mean-Field Regimes in Spatial Networks

Bonamassa, Ivan; Gross, Bnaya; Danziger, Michael M.; Havlin, Shlomo

doi:10.1103/physrevlett.123.088301

Cited by 20 publications

(24 citation statements)

References 43 publications

(54 reference statements)

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“…The homogeneous model has been studied in [18] so here we will study the heterogeneous spatial modular model. We study the model under percolation process at which a fraction 1 − p of nodes are randomly removed from the network.…”

Section: Analytical and Numerical Results Of Percolation In The Hetermentioning

confidence: 99%

“…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.…”

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confidence: 99%

“…However, they are different in the assignment of the links. Our model has heterogeneous structure since it is divided into communities or cities whereas the model in [18] has an homogeneous structure. Thus, we will refer to them as the heterogeneous model here and the homogeneous model in [18].…”

mentioning

confidence: 99%

“…Our model has heterogeneous structure since it is divided into communities or cities whereas the model in [18] has an homogeneous structure. Thus, we will refer to them as the heterogeneous model here and the homogeneous model in [18]. We find that while in the homogeneous structure one observes critical stretching, in contrast, the heterogeneous structure studied here, do not experience such a phenomena due to the two distinct transitions.…”

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confidence: 99%

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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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Section: Analytical and Numerical Results Of Percolation In The Hetermentioning

confidence: 99%

Section: Heterogeneous and Homogeneous Spatial Modelsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Two transitions in spatial modular networks

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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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