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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 cooperativeâ€¦ (More)

- Sergey N. Dorogovtsev, Alexander V. Goltsev, Jose F. F. Mendes
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2002

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), whichâ€¦ (More)

- Alexander V. Goltsev, Sergey N. Dorogovtsev, J. G. Oliveira, Jose F. F. Mendes
- Physical review letters
- 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 diseasesâ€¦ (More)

- Gareth J. Baxter, Sergey N. Dorogovtsev, Alexander V. Goltsev, Jose F. F. Mendes
- Physical review letters
- 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 clustersâ€¦ (More)

- Sergey N. Dorogovtsev, Alexander V. Goltsev, Jose F. F. Mendes
- Physical review letters
- 2006

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 atâ€¦ (More)

- Gareth J. Baxter, Sergey N. Dorogovtsev, Alexander V. Goltsev, Jose F. F. Mendes
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2011

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 hasâ€¦ (More)

- Sergey N. Dorogovtsev, Alexander V. Goltsev, Jose F. F. Mendes, A. N. Samukhin
- Physical review. E, Statistical, nonlinear, andâ€¦
- 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.â€¦ (More)

- Sergey N. Dorogovtsev, Alexander V. Goltsev, Jose F. F. Mendes
- Physical review. E, Statistical, nonlinear, andâ€¦
- 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 anomalousâ€¦ (More)

Ferroelectromagnets are an interesting group of compounds that complement purely (anti-)ferroelectric or (anti-)ferromagnetic materialsâ€”they display simultaneous electric and magnetic order. Withâ€¦ (More)

- Alexander V. Goltsev, Sergey N. Dorogovtsev, Jose F. F. Mendes
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2006

We develop the theory of the -core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the -core percolation is an unusual, hybrid phaseâ€¦ (More)