Critical thinking of scale-free networks: similarities and differences in power-law random graphs

We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.

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Optimal shattering of complex networks

Applied Network Science ◽

10.1007/s41109-019-0205-5 ◽

2019 ◽

Vol 4 (1) ◽

Author(s):

Nicole Balashov ◽

Reuven Cohen ◽

Avieli Haber ◽

Michael Krivelevich ◽

Simi Haber

Keyword(s):

Complex Networks ◽

Random Graphs ◽

Polynomial Time ◽

Optimal Performance ◽

Regular Graphs ◽

Scale Free ◽

Scale Free Networks ◽

Minimum Number

Abstract We consider optimal attacks or immunization schemes on different models of random graphs. We derive bounds for the minimum number of nodes needed to be removed from a network such that all remaining components are fragments of negligible size.We obtain bounds for different regimes of random regular graphs, Erdős-Rényi random graphs, and scale free networks, some of which are tight. We show that the performance of attacks by degree is bounded away from optimality.Finally we present a polynomial time attack algorithm and prove its optimal performance in certain cases.

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Effect of connection on transport between scale free networks

International Journal of Modern Physics C ◽

10.1142/s0129183117500644 ◽

2017 ◽

Vol 28 (05) ◽

pp. 1750064 ◽

Cited By ~ 5

Author(s):

A. Ould Baba ◽

O. Bamaarouf ◽

A. Rachadi ◽

H. Ez-Zahraouy

Keyword(s):

Numerical Simulations ◽

Power Law ◽

Preferential Attachment ◽

Electrical Conductance ◽

Global Network ◽

Scale Free ◽

Scale Free Networks ◽

Conductance Distribution

Using numerical simulations, we investigate the effects of the connectivity and topologies of network on the quality of transport between connected scale free networks. Hence, the flow as the electrical conductance between connected networks is calculated. It is found that the conductance distribution between networks follow a power law [Formula: see text] where [Formula: see text] is the exponent of the global Network of network, we show that the transport in the symmetric growing preferential attachment connection is more efficient than the symmetric static preferential attachment connection. Furthermore, the differences of transport and networks communications properties in the different cases are discussed.

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Scale-Free Networks Based on the Value of Interest

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.753-755.2959 ◽

2013 ◽

Vol 753-755 ◽

pp. 2959-2962

Author(s):

Jun Tao Yang ◽

Hui Wen Deng

Keyword(s):

Network Model ◽

Power Law ◽

Scale Free Network ◽

Power Law Distribution ◽

Scale Free ◽

Distribution Property ◽

Scale Free Networks ◽

Free Model ◽

Free Network ◽

Interest Model

Assigning the value of interest to each node in the network, we give a scale-free network model. The value of interest is related to the fitness and the degree of the node. Experimental results show that the interest model not only has the characteristics of the BA scale-free model but also has the characteristics of fitness model, and the network has a power-law distribution property.

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The use of the power law for designing wireless networks

ITM Web of Conferences ◽

10.1051/itmconf/20182100012 ◽

2018 ◽

Vol 21 ◽

pp. 00012

Author(s):

Andrzej Paszkiewicz

Keyword(s):

Wireless Networks ◽

Power Law ◽

Degree Distribution ◽

Limited Resources ◽

Random Networks ◽

New Approach ◽

Available Bandwidth ◽

Scale Free ◽

Scale Free Networks ◽

Node Removal

The paper concerns the use of the scale-free networks theory and the power law in designing wireless networks. An approach based on generating random networks as well as on the classic Barabási-Albert algorithm were presented. The paper presents a new approach taking the limited resources for wireless networks into account, such as available bandwidth. In addition, thanks to the introduction of opportunities for dynamic node removal it was possible to realign processes occurring in wireless networks. After introduction of these modifications, the obtained results were analyzed in terms of a power law and the degree distribution of each node.

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GROWING HIERARCHICAL SCALE-FREE NETWORKS BY MEANS OF NONHIERARCHICAL PROCESSES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018518 ◽

2007 ◽

Vol 17 (07) ◽

pp. 2447-2452 ◽

Cited By ~ 10

Author(s):

S. BOCCALETTI ◽

D.-U. HWANG ◽

V. LATORA

Keyword(s):

Power Law ◽

Degree Distribution ◽

Preferential Attachment ◽

Rate Equations ◽

Scale Free ◽

Scale Free Networks ◽

Degree Correlations ◽

Law Degree ◽

Hierarchical Scale

We introduce a fully nonhierarchical network growing mechanism, that furthermore does not impose explicit preferential attachment rules. The growing procedure produces a graph featuring power-law degree and clustering distributions, and manifesting slightly disassortative degree-degree correlations. The rigorous rate equations for the evolution of the degree distribution and for the conditional degree-degree probability are derived.

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A process of rumour scotching on finite populations

Royal Society Open Science ◽

10.1098/rsos.150240 ◽

2015 ◽

Vol 2 (9) ◽

pp. 150240 ◽

Cited By ~ 4

Author(s):

Guilherme Ferraz de Arruda ◽

Elcio Lebensztayn ◽

Francisco A. Rodrigues ◽

Pablo Martín Rodríguez

Keyword(s):

Monte Carlo ◽

Random Graphs ◽

Information Dissemination ◽

Initial Conditions ◽

Qualitative Behaviour ◽

Analytical Treatment ◽

Scale Free ◽

Pairwise Interactions ◽

Scale Free Networks ◽

Optimal Information

Rumour spreading is a ubiquitous phenomenon in social and technological networks. Traditional models consider that the rumour is propagated by pairwise interactions between spreaders and ignorants. Only spreaders are active and may become stiflers after contacting spreaders or stiflers. Here we propose a competition-like model in which spreaders try to transmit an information, while stiflers are also active and try to scotch it. We study the influence of transmission/scotching rates and initial conditions on the qualitative behaviour of the process. An analytical treatment based on the theory of convergence of density-dependent Markov chains is developed to analyse how the final proportion of ignorants behaves asymptotically in a finite homogeneously mixing population. We perform Monte Carlo simulations in random graphs and scale-free networks and verify that the results obtained for homogeneously mixing populations can be approximated for random graphs, but are not suitable for scale-free networks. Furthermore, regarding the process on a heterogeneous mixing population, we obtain a set of differential equations that describes the time evolution of the probability that an individual is in each state. Our model can also be applied for studying systems in which informed agents try to stop the rumour propagation, or for describing related susceptible–infected–recovered systems. In addition, our results can be considered to develop optimal information dissemination strategies and approaches to control rumour propagation.

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