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Critical phenomena in complex networks
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from thos…
k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
A. V. Goltsev, S. N. Dorogovtsev, J. F. F. Mendes
We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual,…
k-core organization of complex networks
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
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 w…
Correlations in interacting systems with a network topology
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins),…