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Deterministic scalefree networks
 PHYSICA A29 (2001) 5591)
, 2001
"... Scalefree networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scalefree topology are stochastic, that is they create networks in which the nodes appear ..."
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Cited by 260 (1 self)
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appear to be randomly connected to each other. Here we propose a simple model that generates scalefree networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.
Epidemic Spreading in ScaleFree Networks
, 2000
"... The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scalefree networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from c ..."
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Cited by 550 (14 self)
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The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scalefree networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from
Deterministic ScaleFree Networks
, 2002
"... Scalefree networks are abundant in nature, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scalefree topology are stochastic, that is they create networks in which the nodes appear to be rando ..."
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to be randomly connected to each other. Here we propose a simple model that generates scalefree networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.
Scalefree characteristics of random networks: The topology of the worldwide web
 PHYSICA A
, 2000
"... The worldwide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scalefree characteristics. We introduce a mod ..."
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Cited by 351 (0 self)
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model that leads to a scalefree network, capturing in a minimal fashion the selforganization processes governing the worldwide web.
ScaleFree Network in
 Stock Markets,” J. Korean Physical Society
, 2002
"... A unified architecture for agent behaviors with selection of evolved ..."
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Cited by 2 (0 self)
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A unified architecture for agent behaviors with selection of evolved
Scalefree percolation
, 2011
"... We formulate and study a model for inhomogeneous longrange percolation on Zd. Each vertex x ∈ Zd is assigned a nonnegative weight Wx, where (Wx) x∈Zd are i.i.d. random variables. Conditionally on the weights, and given two parameters α, λ> 0, the edges are independent and the probability that t ..."
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Cited by 8 (3 self)
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We formulate and study a model for inhomogeneous longrange percolation on Zd. Each vertex x ∈ Zd is assigned a nonnegative weight Wx, where (Wx) x∈Zd are i.i.d. random variables. Conditionally on the weights, and given two parameters α, λ> 0, the edges are independent and the probability that there is an edge between x and y is given by pxy = 1 − exp{−λWxWy/x − y  α}. The parameter λ is the percolation parameter, while α describes the longrange nature of the model. We focus on the degree distribution in the resulting graph, on whether there exists an infinite component and on graph distance between remote pairs of vertices. First, we show that the tail behavior of the degree distribution is related to the tail behavior of the weight distribution. When the tail of the distribution of Wx is regularly varying with exponent τ − 1, then the tail of the degree distribution is regularly varying with exponent γ = α(τ − 1)/d. The parameter γ turns out to be crucial for the behavior of the model. Conditions on the weight distribution and γ are formulated for the existence of a critical value λc ∈ (0, ∞) such that the graph contains an infinite component when λ> λc and no infinite component when λ < λc. Furthermore, a phase transition is established for the graph distances between vertices in the infinite component at the point γ = 2, that is, at the point where the degrees switch from having finite to infinite second moment. The model can be viewed as an interpolation between longrange percolation and models for inhomogeneous random graphs, and we show that the behavior shares the interesting features of both these models.
Epidemics and immunization in scalefree networks
 IN: BORNHOLDT S, AND SCHUSTER H G (EDS.) HANDBOOK OF GRAPH AND NETWORKS
, 2003
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