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- Publications
- Influence

Critical phenomena in complex networks

- S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Computer Science, Physics
- ArXiv
- 30 April 2007

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 cooperative… Expand

Pseudofractal scale-free web.

- S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Medicine, Physics
- Physical review. E, Statistical, nonlinear, and…
- 8 December 2001

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), which… Expand

Localization and Spreading of Diseases in Complex Networks

- A. Goltsev, S. N. Dorogovtsev, J. G. Oliveira, J. F. Mendes
- Computer Science, Physics
- Physical review letters
- 20 February 2012

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 diseases… Expand

Spectra of complex networks.

- S. N. Dorogovtsev, A. Goltsev, J. Mendes, A. N. Samukhin
- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and…
- 12 June 2003

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

K-core Organization of Complex Networks

- S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Medicine, Computer Science
- Physical review letters
- 5 September 2005

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 at… Expand

Explosive percolation transition is actually continuous.

- R. A. da Costa, S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Physics, Mathematics
- Physical review letters
- 13 September 2010

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

Heterogeneous k-core versus bootstrap percolation on complex networks.

- G. Baxter, S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and…
- 20 December 2010

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 has… Expand

Piezoelectricity and Crystal Symmetry

- A. L. Kholkin, N. Pertsev, A. Goltsev
- Materials Science
- 2008

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 of… Expand

Avalanche collapse of interdependent networks.

- G. Baxter, S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Medicine, Physics
- Physical review letters
- 2 July 2012

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 clusters… Expand

Ising Model on Networks with an Arbitrary Distribution of Connections

- S. N. Dorogovtsev, A. Goltsev, J. Mendes
- Medicine, Physics
- Physical review. E, Statistical, nonlinear, and…
- 11 March 2002

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 anomalous… Expand