Numerical simulations of the phase transition property of the explosive percolation model on Erds Rnyi random network

Li, Yan; Gang, Tang; Li-Jiang, Song; Xun, Zhipeng; Xia, Hui; Hao, Dapeng

doi:10.7498/aps.62.046401

Cited by 10 publications

(3 citation statements)

References 29 publications

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“…Consequently, the network is disordered and there is no difference between nodes. In the ER network, [34,35] the connections between nodes are random. Hence, the nodes of the ER network have a slight difference from each other.…”

Section: Analysis Of the Spatial Networkmentioning

confidence: 99%

Analysis of overload-based cascading failure in multilayer spatial networks*

et al. 2020

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Many complex networks in real life are embedded in space and most infrastructure networks are interdependent, such as the power system and the transport network. In this paper, we construct two cascading failure models on the multilayer spatial network. In our research, the distance l between nodes within the layer obeys the exponential distribution P(l) ∼ exp(–l/ζ), and the length r of dependency link between layers is defined according to node position. An entropy approach is applied to analyze the spatial network structure and reflect the difference degree between nodes. Two metrics, namely dynamic network size and dynamic network entropy, are proposed to evaluate the spatial network robustness and stability. During the cascading failure process, the spatial network evolution is analyzed, and the numbers of failure nodes caused by different reasons are also counted, respectively. Besides, we discuss the factors affecting network robustness. Simulations demonstrate that the larger the values of average degree 〈k〉, the stronger the network robustness. As the length r decreases, the network performs better. When the probability p is small, as ζ decreases, the network robustness becomes more reliable. When p is large, the network robustness manifests better performance as ζ increases. These results provide insight into enhancing the robustness, maintaining the stability, and adjusting the difference degree between nodes of the embedded spatiality systems.

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Section: Analysis Of the Spatial Networkmentioning

confidence: 99%

Analysis of overload-based cascading failure in multilayer spatial networks*

et al. 2020

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“…Following the same method, we can also get the GMCC in the two-layer Erdos Rnyi (ER) network, [32,33] which is a typical random network. The only difference is that the degree distribution of ER network is…”

Section: The Cascading Model In the Two-layer Networkmentioning

confidence: 99%

Cascading failure in multilayer networks with dynamic dependency groups

et al. 2018

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The cascading failure often occurs in real networks. It is significant to analyze the cascading failure in the complex network research. The dependency relation can change over time. Therefore, in this study, we investigate the cascading failure in multilayer networks with dynamic dependency groups. We construct a model considering the recovery mechanism. In our model, two effects between layers are defined. Under Effect 1, the dependent nodes in other layers will be disabled as long as one node does not belong to the largest connected component in one layer. Under Effect 2, the dependent nodes in other layers will recover when one node belongs to the largest connected component. The theoretical solution of the largest component is deduced and the simulation results verify our theoretical solution. In the simulation, we analyze the influence factors of the network robustness, including the fraction of dependent nodes and the group size, in our model. It shows that increasing the fraction of dependent nodes and the group size will enhance the network robustness under Effect 1. On the contrary, these will reduce the network robustness under Effect 2. Meanwhile, we find that the tightness of the network connection will affect the robustness of networks. Furthermore, setting the average degree of network as 8 is enough to keep the network robust.

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“…The percolation phase transition of a network through the gradual addition of links is used in many fields to model dynamics, such as social networks, physical systems, epidemics and spread of infectious diseases, and porous media. [1][2][3][4][5][6] A lot of papers have paid attention to whether or not the explosive percolation transition with the other growth rules [7][8][9][10][11][12][13][14][15] is continuous [16][17][18][19][20][21] since certain Achlioptas processes exhibit this phenomenon. [17] The model is considered as adding edges from N isolated vertices, where N is very large.…”

Section: Introductionmentioning

confidence: 99%

Characteristics of phase transitions via intervention in random networks

et al. 2014

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We present a percolation process in which the classical Erdös—Rényi (ER) random evolutionary network is intervened by the product rule (PR) from some moment t0. The parameter t0 is continuously tunable over the real interval [0, 1]. This model becomes the random network under the Achlioptas process at t0 = 0 and the ER network at t0 = 1. For the percolation process at t0 ≤ 1, we introduce a relatively slow-growing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at t0 ≤ 0.5. We take the relatively slow-growing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about t0. This contributes to understanding the rapid mergence of the large clusters at the critical point. The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When t0 > 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slow-growing point, the duration of the relatively slow-growing process, as well as the relatively maximum strength between the percolation percolation at t0 < 1 and the ER network about different t0. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.

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Numerical simulations of the phase transition property of the explosive percolation model on Erds Rnyi random network

Cited by 10 publications

References 29 publications

Analysis of overload-based cascading failure in multilayer spatial networks*

Analysis of overload-based cascading failure in multilayer spatial networks*

Cascading failure in multilayer networks with dynamic dependency groups

Characteristics of phase transitions via intervention in random networks

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