Complex networks: Effect of subtle changes in nature of randomness

Goswami, Sanchari; Biswas, Soham; Sen, Parongama

doi:10.1016/j.physa.2010.10.024

Cited by 6 publications

(14 citation statements)

References 18 publications

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“…The study made with much larger networks indicated that the network had finite dimensional behavior for 1 ≤ δ < 2 [45] while in [44], it was claimed that up to δ = 2, the small world behavior exists. In a more recent work [29], all possible shortest paths were evaluated numerically using a burning algorithm, and it was again found that the network retains the small world property up to δ = 2 while the clustering coefficient vanishes below δ = 1. Such a result was also obtained in [46].…”

Section: A Earlier Studies On This Network: Static Propertiesmentioning

confidence: 99%

The susceptible–infected–recovered model on a Euclidean network

Khaleque¹,

Sen²

2013

J. Phys. A: Math. Theor.

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We consider the Susceptible-Infected-Recovered (SIR) epidemic model on a Euclidean network in one dimension in which nodes at a distance l are connected with probability P (l) ∝ l −δ in addition to nearest neighbors. The topology of the network changes as δ is varied and its effect on the SIR model is studied. R(t), the recovered fraction of population up to time t, and τ , the total duration of the epidemic are calculated for different values of the infection probability q and δ. A threshold behavior is observed for all δ up to δ ≈ 2.0; above the threshold value q = qc, the saturation value Rsat attains a finite value. Both Rsat and τ show scaling behavior in a finite system of size N ;. qc is constant for 0 ≤ δ < 1 and increases with δ for 1 < δ 2. Mean field behavior is seen up to δ ≈ 1.3; weak dependence on δ is observed beyond this value of δ. The distribution of the outbreak sizes is also estimated and found to be unimodal for q < qc and bimodal for q > qc. The results are compared to static percolation phenomena and also to mean field results for finite systems. Discussions on the properties of the Euclidean network are made in the light of the present results.

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Section: A Earlier Studies On This Network: Static Propertiesmentioning

confidence: 99%

The susceptible–infected–recovered model on a Euclidean network

Khaleque¹,

Sen²

2013

J. Phys. A: Math. Theor.

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“…Random model A is a variant of the WS model with identical static properties. It is regular for p = 0, random for p = 1, and for any p > 0, the nature of RMA is small-worldlike [13,16]. Euclidean models of RMB type have been studied in a few earlier works [16][17][18].…”

Section: Description Of the Network Modelsmentioning

confidence: 99%

“…It is regular for p = 0, random for p = 1, and for any p > 0, the nature of RMA is small-worldlike [13,16]. Euclidean models of RMB type have been studied in a few earlier works [16][17][18]. While it is more or less agreed that for α 1 the network is random and for α > 2 it behaves as a regular network, the nature of the network for intermediate values of α is not very well understood.…”

Section: Description Of the Network Modelsmentioning

confidence: 99%

Effect of the nature of randomness on quenching dynamics of the Ising model on complex networks

Biswas

Sen²

2011

Phys. Rev. E

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Randomness is known to affect the dynamical behavior of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero-temperature quench of the Ising model on two types of random networks. In both networks, which are embedded in a one-dimensional space, the first-neighbor connections exist and the average degree is 4 per node. In random model A the second-neighbor connections are rewired with a probability p, while in random model B additional connections between neighbors at a Euclidean distance l(l > 1) are introduced with a probability P(l) proportionally l(-α). We find that for both models, the dynamics leads to freezing such that the system gets locked in a disordered state. The point at which the disorder of the nonequilibrium steady state is maximum is located. The behavior of dynamical quantities such as residual energy, order parameter, and persistence are discussed and compared. Overall, the behavior of physical quantities are similar, although subtle differences are observed due to the difference in the nature of randomness.

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“…The fact that results do not depend on the system size undermines our predictions that the average path length l itself determines if all mapping methods overlap or not, because the l increases with the system size [35]. However, one should probably not look at the path length itself but at the relative path length, which is defined as the average path length of a given network divided by the average path length of a random network of the same size and average degree.…”

Section: Resultsmentioning

confidence: 83%

Mapping the q-voter model: From a single chain to complex networks

Jędrzejewski

Sznajd-Weron

Szwabiński

2016

Physica A: Statistical Mechanics and its Applications

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We propose and compare six different ways of mapping the modified q-voter model to complex networks. Considering square lattices, Barabási-Albert, Watts-Strogatz and real Twitter networks, we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level. Using Monte Carlo simulations we show that the answer depends on the relative average path length of the network and for real-life topologies the differences between the considered mappings may be negligible.

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Complex networks: Effect of subtle changes in nature of randomness

Cited by 6 publications

References 18 publications

The susceptible–infected–recovered model on a Euclidean network

The susceptible–infected–recovered model on a Euclidean network

Effect of the nature of randomness on quenching dynamics of the Ising model on complex networks

Mapping the q-voter model: From a single chain to complex networks

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