World Wide Web scaling exponent from Simon’s 1955 model

Bornholdt, Stefan; Ebel, Holger

doi:10.1103/physreve.64.035104

Cited by 117 publications

(105 citation statements)

References 15 publications

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“…The probability that a node obtains an additional link is proportional to its current degree. It can be interpreted as an application of Simon's growth model in the context of networks [20,21], readily explaining the emergent scaling in the degree distribution. The BA-model has been successively modified reproducing the scale-free behavior of the connectivity distribution [22][23][24].…”

Section: Previous Modelsmentioning

confidence: 99%

Highly clustered scale-free networks

Klemm¹,

2002

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We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate. Notably, the degree distribution is conserved even though only the most recently grown part of the network is considered. This feature is relevant because real-world networks truncated in the same way exhibit a power-law distribution in the degree. As the network grows, the clustering reaches an asymptotic value larger than for regular lattices of the same average connectivity. These highclustering scale-free networks indicate that memory effects could be crucial for a correct description of the dynamics of growing networks.Many systems can be represented by networks, i.e. as a set of nodes joined together by links. Social networks, the Internet, food webs, distribution networks, metabolic and protein networks, the networks of airline routes, scientific collaboration networks and citation networks are just some examples of such systems [1][2][3][4][5][6][7][8][9][10][11]. Recently it has been observed that a variety of networks exhibit topological properties that deviate from those predicted by random graphs [1,2]. For instance, real networks display clustering higher than expected for random networks [4]. Also, it has been found that many large networks are scale-free. Their degree distribution decays as a powerlaw that cannot be accounted for by the Poisson distribution of random graphs [12,13]. The type of the degree distribution is of great importance for the functionality of the network [14][15][16]. Beside the degree distribution, other features of the growth dynamics of real-world networks are currently under investigation. For citation networks, the Internet, and collaboration networks of scientists and actors, it has been shown [17,18] that the probability for a node to obtain a new link is an increasing function of the number of links the node already has. This feature of the dynamics is called preferential attachment. Furthermore the aging of nodes is of particular interest [19]. In the network of scientific collaborations, every node stops receiving links a finite time after it has been added to the network, since scientists have a finite time span of being active. Similarly, in citation networks, papers cease to receive links (citations), because their contents are outdated or summarized in review articles, which are then cited instead. Whether a paper is still cited or not, depends on a collective memory containing the popularity of the paper.In the current paper we address the study of growing complex networks from the perspective of the memory of the nodes. First, we present empirical evidence for the age dependence of the growth dynamics of the network of scientific citations. We find that old nodes are less likely to obtain links than nodes added to the network more recently. Second, motivated by this ...

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Section: Previous Modelsmentioning

confidence: 99%

Highly clustered scale-free networks

Klemm¹,

2002

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“…Discussion of the growth of the WWW may be found in Refs. [27,28]. Suppose, you want to create your own personal home page.…”

Section: Reasons For the Accelerationmentioning

confidence: 99%

Accelerated growth of networks

Dorogovtsev¹,

Mendes²

2002

Handbook of Graphs and Networks

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“…This corresponds to Simon's general model for such copy and growth processes [14,15]. Let us briefly apply this model to the e-mail network.…”

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confidence: 99%

“…Let us briefly apply this model to the e-mail network. From our data we estimated the ratio of the growth rate of nodes to the growth rate of links to α =0.597 nodes per links which is sufficient to calculate the scaling exponent γ [15]:…”

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confidence: 99%

Scale-free topology of e-mail networks

2002

Self Cite

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We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in other social networks. These observations imply that the spreading of e-mail viruses is greatly facilitated in real e-mail networks compared to random architectures.Comment: 4 pages RevTeX, 4 figures PostScript (extended version

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World Wide Web scaling exponent from Simon’s 1955 model

Cited by 117 publications

References 15 publications

Highly clustered scale-free networks

Highly clustered scale-free networks

Accelerated growth of networks

Scale-free topology of e-mail networks

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