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Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperativeExpand
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Pseudofractal scale-free web.
We find that scale-free random networks are excellently modeled by simple deterministic graphs. Our graph has a discrete degree distribution (degree is the number of connections of a vertex), whichExpand
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Localization and Spreading of Diseases in Complex Networks
Using the susceptible-infected-susceptible model on unweighted and weighted networks, we consider the disease localization phenomenon. In contrast to the well-recognized point of view that diseasesExpand
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Spectra of complex networks.
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local treelike structure), exact equations are derived.Expand
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K-core Organization of Complex Networks
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures--k-cores. The k-core is the largest subgraph where vertices have atExpand
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Explosive percolation transition is actually continuous.
Recently a discontinuous percolation transition was reported in a new "explosive percolation" problem for irreversible systems [D. Achlioptas, R. M. D'Souza, and J. Spencer, Science 323, 1453 (2009)]Expand
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Heterogeneous k-core versus bootstrap percolation on complex networks.
We introduce the heterogeneous k-core, which generalizes the k-core, and contrast it with bootstrap percolation. Vertices have a threshold r(i), that may be different at each vertex. If a vertex hasExpand
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Piezoelectricity and Crystal Symmetry
In this chapter, the symmetry aspects of the piezoelectric effect in various materials (single crystals, ceramics, and thin films) are briefly overviewed. First, the third-rank tensor ofExpand
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Avalanche collapse of interdependent networks.
We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clustersExpand
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Ising Model on Networks with an Arbitrary Distribution of Connections
We find the exact critical temperature T(c) of the nearest-neighbor ferromagnetic Ising model on an "equilibrium" random graph with an arbitrary degree distribution P(k). We observe an anomalousExpand
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