Evolution of networks

By Sergey N. Dorogovtsev, José Fernando Ferreira Mendes. 2001

3,319 citations recorded by the source corpus.

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, and so on.

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0c328305157932a3560fb202a77f155c359a8620

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Citations in the corpus

Community detection in graphs (2009, background): “…degree distributions have for the structure and function of real networks (Albert and Barabási, 2002; Barrat et al., 2008; Boccaletti et al., 2006; Dorogovtsev and Mendes, 2002; Newman, 2003; Pastor-Satorras and Vespignani, 2004), it is preferable to go for a null model with the same degree…”
Robustness and Vulnerability of Scale-Free Random Graphs (2004, methodology): “For heuristic and experimental studies of the Barab´asi-Albert model, we refer the reader to the extensive surveys [Albert and Barab´asi 02] and [Dorogovtsev and Mendes 02]; these references also describe many generalizations, and contain much background material on the by now rather large subject…”
On the Embeddability of Random Walk Distances (2013, methodology): “Finally, as a representative of a planar graph, we add a synthetic graph generated by the DorogovtsevGoltsev-Mendes Internet model [12].”
Invariant properties in coevolutionary networks of plant-animal interactions (2002, methodology): “These generalized patterns, specially the power-law (or scale-free) topologies lead to small-world patterns with important implications for the evolution, stability, and resilience to perturbations of these networks (Barabási & Albert 1999; Albert & Barabási 2002; Dorogovtsev & Mendes 2002).”
Knowledge transfer in a tourism destination: the effects of a network structure (2009, background): “It should be noticed that both values are lower than those reported by the literature for social networks (Dorogovtsev & Mendes, 2002; Watts, 2004).”
Statistical physics of vaccination (2016, background): “It relies on underlying transmission routes to control further spread without even any information on epidemiology of the infectious disease [167].”
The phase transition in inhomogeneous random graphs (2005, background): “Perhaps the most striking and important result of Erd˝ os and Rényi concerns the sudden emergence of the 'giant component', the phase transition in G(n, p) that occurs at p = 1/n: if c > 0 is a constant, then the largest B ´ ELA BOLLOB´AS , SVANTE JANSON, AND OLIVER RIORDAN component of G(n, c/n)…”
Catastrophic cascade of failures in interdependent networks (2009, background): “from those of single-network systems. In this article, these results are reviewed and the main properties discussed. 1. – Introduction The last decade witnessed an intensive study of complex networks [1, 2, 3, 4, 5, 6] boosted by several real-world data revealing complex structures in the topology o”
Self-similar community structure in a network of human interactions. (2002, methodology): “We analyse the complex e-mail network of a real organisation with about 1,700 employees and determine its community structure [6, 7, 8, 9].”