Numerical evaluation of the upper critical dimension of percolation in scale-free networks

Wu, Zhenhua J.; Lagorio, C.; Braunstein, Lidia A.; Cohen, Reuven; Havlin, Shlomo; Stanley, H. Eugene

doi:10.1103/physreve.75.066110

Cited by 26 publications

(18 citation statements)

References 19 publications

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“…The prediction in the regime 2< γ <3 is obtained by accounting for the divergence of the second moment of the degree distribution with cutoff given by . The prediction in the regime 3< γ ≤4 has been obtained by Wu et al 17 For γ ≥4 instead, the exponent ν equals its mean-field value.…”

Section: Methodsmentioning

confidence: 76%

Breaking of the site-bond percolation universality in networks

Radicchi

Castellano

2015

Nat Commun

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The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system. Percolation has always been regarded as a substrate-dependent but model-independent process, in the sense that the critical exponents of the transition are determined by the geometry of the system, but they are identical for the bond and site percolation models. Here, we report a violation of such assumption. We provide analytical and numerical evidence of a difference in the values of the critical exponents between the bond and site percolation models in networks with null percolation thresholds, such as scale-free graphs with diverging second moment of the degree distribution. We discuss possible implications of our results in real networks, and provide additional insights on the anomalous nature of the percolation transition with null threshold.

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Section: Methodsmentioning

confidence: 76%

Breaking of the site-bond percolation universality in networks

Radicchi

Castellano

2015

Nat Commun

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“…Thus, in these cases, the trap will be attached to a sufficient number of links for the scaling t tr ∼ N γ−2 γ−1 to appear. The value of γ for which SF networks are equivalent to ER networks is a topic of recent interest [36]. Our results suggest that SF networks are equivalent to ER only when γ is infinite, since only when γ → ∞ does β → 1, as for homogenous ER networks.…”

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confidence: 70%

Trapping in complex networks

et al. 2008

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We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density ρ(t) of random walkers in the presence of one or multiple traps with concentration c. We show using theory and simulations that in ER networks, while for short times ρ(t) ∝ exp(−Act), for longer times ρ(t) exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: ρ(t) is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we findIntroduction. -The properties of random walk greatly vary depending on the dimension and the structure of the medium in which it is confined [1][2][3][4], where a particularly interesting medium for the study of the random walk is complex networks [5][6][7][8][9]. Networks describe systems from various fields, such as communication (e.g. the Internet), the social sciences, transportation, biology, and others. Many of these networks are scale-free (SF) [10][11][12][13]. This class of networks is defined by a broad degree distribution, such as a power law P (k) ∝ k −γ (k ≥ m), where γ is a parameter which controls the broadness of the distribution.Trapping is a random walk problem in which traps are placed in random locations, absorbing all walkers that visit them. This problem was shown to yield different results over different geometries, dimensions and time regimes [2,3,[14][15][16][17]. The main property of interest during such a process is the survival probability ρ(t), which denotes the probability that a particle survives after t steps. The problem was studied in regular lattices and in fractal spaces [2,[14][15][16][17][18][19] and recently, in small-world networks [6].In this Letter we study the problem of trapping in networks. This is a model for the propagation of information in certain communication networks. This follows since in some cases data packets traverse the network in a random fashion (for example, in wireless sensor networks [20], ad-hoc networks [21] and peer-to-peer networks [22]). A malfunctioning node in which information is lost (e.g., a router which cannot transmit data due to some failure) acts just like a trap in the model. This model can also be applied to loss of information in messages over communication systems, e.g. in the case of e-mail messages, where a malfunctioning e-mail server acts as a node absorbing, but not transmitting, all e-mail

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“…does not hold and the only magnitude that matters is T , which has to be measured by the peak of the second giant component [25]. In those cases, for σ c = 1 we have to use Eq.…”

Section: Table Imentioning

confidence: 99%

Intermittent social distancing strategy for epidemic control

2012

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We study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks. We characterize the effect of our strategy in the framework of the susceptible-infected-recovered model. In our model, based on local information, a susceptible individual interrupts the contact with an infected individual with a probability σ and restores it after a fixed time t b . We find that, depending on the network topology, in our social distancing strategy there exists a cutoff threshold σ c beyond which the epidemic phase disappears. Our results are supported by a theoretical framework and extensive simulations of the model. Furthermore we show that this strategy is very efficient because it leads to a "susceptible herd behavior" that protects a large fraction of susceptibles individuals. We explain our results using percolation arguments.

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Numerical evaluation of the upper critical dimension of percolation in scale-free networks

Cited by 26 publications

References 19 publications

Breaking of the site-bond percolation universality in networks

Breaking of the site-bond percolation universality in networks

Trapping in complex networks

Intermittent social distancing strategy for epidemic control

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