Connectivity distribution and attack tolerance of general networks with both preferential and random attachments

Liu, Zonghua; Lai, Ying–Cheng; Ye, Nong; Dasgupta, Partha

doi:10.1016/s0375-9601(02)01317-8

Cited by 135 publications

(79 citation statements)

References 23 publications

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“…Though the BA model captures those fundamental mechanisms, it only predicts a fixed exponent, while real networks display various exponents. Therefore, many scientists [4][5][6][7][8][9][10][11][12][13] have proposed some extensions to make the models more realistic.…”

Section: Introductionmentioning

confidence: 99%

Local preferential attachment model for hierarchical networks

Wang

Guo

Yang

et al. 2009

Physica A: Statistical Mechanics and its Applications

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In real-life networks, incomers may only connect to a few others in a local area for their limited information, and individuals in a local area are likely to have close relations. Accordingly, we propose a local preferential attachment model. Here, a local-area-network stands for a node and all its neighbors, and the new nodes perform nonlinear preferential, in local areas. The stable degree distribution and clusteringdegree correlations are analytically obtained. With the increasing of α, the clustering coefficient increases, while assortativity decreases from positive to negative. In addition, by adjusting the parameter α, the model can generate different kinds of degree distribution, from exponential to power-law. The hierarchical organization, independent of α, is the most significant character of this model.

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Section: Introductionmentioning

confidence: 99%

Local preferential attachment model for hierarchical networks

Wang

Guo

Yang

et al. 2009

Physica A: Statistical Mechanics and its Applications

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“…A recent work [9] indicates that the attachment rule (2) leads to the following connectivity distribution:…”

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confidence: 99%

Topology of the conceptual network of language

et al. 2002

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We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of languages, but also for cognitive science. We study this issue quantitatively, by mapping out the conceptual network of the English language, with the connections being defined by the entries in a Thesaurus dictionary. We find that this network presents a small-world structure, with an amazingly small average shortest path, and appears to exhibit an asymptotic scale-free feature with algebraic connectivity distribution.PACS numbers: 87.23. Ge,89.75.Hc Any language is composed of many thousands of words linked together in an apparently fairly sophisticated way. A language can thus be regarded as a network, in the following sense: (1) the words correspond to nodes of the network, and (2) a link exists between two words if they express similar concepts. Clearly, the underlying network of a language is necessarily sparse in the sense that the average number of links per node is typically much smaller than the total number of nodes. Identifying and understanding the common network topology of languages is of great importance, not only for the study of languages themselves, but also for cognitive science where one of the most fundamental issues concerns associative memory, which is intimately related to the network topology.Recently, there has been a tremendous amount of interest in the study of large, sparse, and complex networks since the seminal papers by Watts and Strogatz [1] on the small-world characteristic and by Barabási and Albert on scale-free features [2]. The small-world concept is static in the sense that it describes the topological property of the network at a given time. Two statistical quantities characterizing a static networks are clustering C and shortest path L , where the former is the probability that any two nodes are connected to each other, given that they are both connected to a common node, and the latter measures the minimal number of links connecting two nodes in the network. Regular networks have high clusterings and small average shortest paths, with random networks at the opposite of the spectrum which have small shortest paths and low clusterings [3]. Small-world networks fall somewhere in between these two extremes. In particular, a network is small world if its clustering coefficient is almost as high as that of a regular network but its average shortest path is almost as small as that of a random network with the same parameters. Watts and Strogatz demonstrated that a small-world network can be easily constructed by adding to a regular network a few additional random links connecting otherwise distant nodes. The scale-free property, on the other hand, is defined by an algebraic behavior in the probability distribution P (k) of k, the number of links at a node in the network. This property is dynamic because it is the consequence of the natural...

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“…In accordance with the BA algorithm, we first construct a SF network with total node number N, average links k, and degree distribution p(k)~k 3 [24,25]. Next, on each node we set a double-well oscillator linked with others, each link having coupling strength λ. Interactions among the oscillators can only occur via these links.…”

Section: Signal Amplification On the Hubmentioning

confidence: 99%

Signal response amplification of scale-free networks

Liu

2011

Chin. Sci. Bull.

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In many animals and insects, hearing is very acute to the faintest of sounds; the underlying mechanism can be explained by self-tuning. Recently, signal response amplification has been shown to be implemented through networks exhibiting scale-free topology, which has potential applications in artificial information processing systems and devices. We review in this paper the main results obtained in networked double-well oscillators and briefly discuss future research directions.signal response, scale-free network, self-tuning, double-well oscillator Citation:Liu Z H. Signal response amplification of scale-free networks. Chinese Sci Bull, 2011Bull, , 56: 3623-3629, doi: 10.1007 Systems that can detect and amplify signals at specific frequencies are commonplace in the natural world and most notably in the visual and auditory systems of animals [1]. Signal detection in animals is through light-and auralsensitive organs, constituted by a large number of networked units. For example, cells in living organisms respond to their environment by an interconnected network of receptors, messengers, protein kinases and other signaling molecules [2][3][4]. One of the more prominent features of our hearing system is the ability to perceive sound stimuli that range over six orders of magnitude in sound pressure [5]. Hair cells within the cochlear are stimulated by sound waves, the induced motion being amplified at characteristic locations that depends on the frequencies of sound. These cells transmit signals to the auditory nerve [6]. It is well known that many animals and insects have the ability to detect faint sounds from their environment. Physiological evidence exists for a range of animals and insect auditory systems that this active audition is due to Hopf bifurcations [7][8][9]. Models have also been proposed to develop the underlying mechanism behind enhanced amplification in hearing systems, i.e. self-tuned critical oscillations of hair cells nearby the Hopf bifurcation. 2 , where a controls the barrier height of the potential; x=±1 are the locations of the two minima. Suppose an oscillator has probability w + (w  ) of jumping from the right (left) well to the left (right) well; then self-tuning means that the parameter a can be self-adjusted by the following equation: a t a t w t p t w t p t twhere p + (p  ) denotes the probability that the oscillator stays at x=±1. If w + and w  are small, the first term in eq.(1) will be larger than the second term and thus result in a decrease in a. For larger w + and w  , the first term in eq.(1) will be smaller than the second term and thus result in an increase in a. Therefore, the parameter a is self-tuned to an optimal value by switching probabilities w + and w  . Scientists and engineers frequently take inspiration from

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Connectivity distribution and attack tolerance of general networks with both preferential and random attachments

Cited by 135 publications

References 23 publications

Local preferential attachment model for hierarchical networks

Local preferential attachment model for hierarchical networks

Topology of the conceptual network of language

Signal response amplification of scale-free networks

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