• Publications
  • Influence
Evolution of networks
TLDR
The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.
Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)
TLDR
The aim of the text is to understand networks and the basic principles of their structural organization and evolution, so even students without a deep knowledge of mathematics and statistical physics will be able to rely on this as a reference.
Critical phenomena in complex networks
TLDR
A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolations, phenomena near epidemic thresholds, condensation transitions,critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned.
Structure of growing networks with preferential linking.
TLDR
The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites and it is shown that the relation beta(gamma-1) = 1 between the exponents is universal.
Pseudofractal scale-free web.
TLDR
It is found that scale-free random networks are excellently modeled by simple deterministic graphs and exactly and numerically with high precision all main characteristics of the graph are found.
Localization and Spreading of Diseases in Complex Networks
TLDR
Using the susceptible-infected-susceptible model on unweighted and weighted networks, the disease localization phenomenon is considered and it is shown that diseases can be localized on a finite number of vertices.
Language as an evolving word web
TLDR
It follows from the theory of the evolution of language that the size of the core part of language, the ‘kernel lexicon’, does not vary as language evolves, and the two regimes in the distribution naturally emerge from the evolutionary dynamics of the word web.
Spectra of complex networks.
TLDR
It is shown that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.
K-core Organization of Complex Networks
TLDR
It is shown that in networks with a finite mean number zeta2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition, and in contrast, ifZeta2 diverges, the networks contain an infinite sequence of k-cores which are ultrarobust against random damage.
Effect of the accelerating growth of communications networks on their structure.
TLDR
It is found that the accelerating growth of networks establishes their structure, and two scenarios of self-organization of nonlinearly growing networks into free-scale structures are considered.
...
1
2
3
4
5
...