Scale-Free Distribution of Avian Influenza Outbreaks

Small, Michael; Walker, David M.; Tse, Chi Kong

doi:10.1103/physrevlett.99.188702

Cited by 96 publications

(67 citation statements)

References 19 publications

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“…Another model applied to SARS spreading of virus in Hong Kong can be found in [405]. In 2007, Small et al [406] studied the distribution of avian influenza virus among wild and domestic birds and obtained a network with scale-free topology with no epidemic threshold. Therefore, local methods could not be used to eradicate the disease, thus pointing to attacks to the hubs as a possible strategy.…”

Section: Epidemic Spreadingmentioning

confidence: 99%

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

Costa

Oliveira

Travieso

et al. 2011

Advances in Physics

656

357

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Section: Epidemic Spreadingmentioning

confidence: 99%

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

Costa

Oliveira

Travieso

et al. 2011

Advances in Physics

656

357

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“…Moreover, they are "large-world", with both of their diameter and average distance increasing as a power function of the network size 47,49,50 . We note that this "large-world" phenomenon was also observed in the global network of avian influenza outbreaks 52,53 .…”

Section: A Construction and Propertiesmentioning

confidence: 96%

Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks

Zhang

Sheng

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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For a random walk on a network, the mean first-passage time from a node i to another node j chosen stochastically according to the equilibrium distribution of Markov chain representing the random walk is called Kemeny constant, which is closely related to the navigability on the network. Thus, the configuration of a network that provides optimal or suboptimal navigation efficiency is a question of interest. It has been proved that complete graphs have the exact minimum Kemeny constant over all graphs. In this paper, by using another method we first prove that complete graphs are the optimal networks with a minimum Kemeny constant, which grows linearly with the network size. Then, we study the Kemeny constant of a class of sparse networks that exhibit remarkable scale-free and fractal features as observed in many real-life networks, which cannot be described by complete graphs. To this end, we determine the closed-form solutions to all eigenvalues and their degeneracies of the networks. Employing these eigenvalues, we derive the exact solution to the Kemeny constant, which also behaves linearly with the network size for some particular cases of networks. We further use the eigenvalue spectra to determine the number of spanning trees in the networks under consideration, which is in complete agreement with previously reported results. Our work demonstrates that scale-free and fractal properties are favorable for efficient navigation, which could be considered when designing networks with high navigation efficiency. Kemeny constant, defined as the mean firstpassage time from a node i to a node j selected randomly according to the equilibrium distribution of Markov chain, is a fundamental quantity for a random walk, since it is a useful indicator characterizing the efficiency of navigation on networks. Here we prove that among all networks, complete graph is the optimal network having the least Kemeny constant, which is consistent with the previous result obtained by a different method. Then, we study the Kemeny constant of a class of sparse scale-free fractal networks, which are ubiquitous in real-life systems. By using the renormalization group technique, we derive the explicit formulas for all eigenvalues and their multiplicities of the networks, based on which we determine the closed-form solution to the Kemeny constant. We show that for some particular cases of networks the leading scaling of Kemeny constant displays the same behavior as that of complete graph, indicating that for networks with a) Electronic mail: zhangzz@fudan.edu.cn; http://homepage.fudan.edu.cn/˜zhangzz/ many nodes, navigation performance similar to that of complete graph can be obtained by networks with many few links. Finally, to show the validity of the eigenvalues and their degeneracies, we also use them to count spanning trees in the networks being studied, and recover previously reported results. Our work is helpful for the structure design of networks where navigation is very efficient.

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“…Given the parallels between the grain size distribution of the crushable DEM model and the Apollonian gasket, it might be expected then that the ultimate contact network induced by comminution should result in a scale-free network with small world properties. It is worth mentioning, however, that typically geographical or spatial scale-free networks are not necessarily small world (e.g., a network constructed from avian flu outbreak data [41]; see also [42]). …”

Section: Evolution To a Scale-free Small World Networkmentioning

confidence: 99%

Complex networks in confined comminution

Walker

Tordesillas²,

Einav³

et al. 2011

Phys. Rev. E

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The physical process of confined comminution is investigated within the framework of complex networks. We first characterize the topology of the unweighted contact networks as generated by the confined comminution process. We find this process gives rise to an ultimate contact network which exhibits a scale-free degree distribution and small world properties. In particular, if viewed in the context of networks through which information travels along shortest paths, we find that the global average of the node vulnerability decreases as the comminution process continues, with individual node vulnerability correlating with grain size. A possible application to the design of synthetic networks (e.g., sensor networks) is highlighted. Next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks, where each link is weighted by the inverse magnitude of the normal force acting at the associated contact. We find that the strong forces (i.e., force chains) are transmitted along pathways in the network which are mainly following shortest-path routing protocols, as typically found, for example, in communication systems. Motivated by our earlier studies of the building blocks for self-organization in dense granular systems, we also explore the properties of the minimal contact cycles. The distribution of the contact strain energy intensity of 4-cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale-free distribution with infinite variance, thereby suggesting that 4-cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking.

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Scale-Free Distribution of Avian Influenza Outbreaks

Cited by 96 publications

References 19 publications

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks

Complex networks in confined comminution

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