Scaling behaviour of developing and decaying networks

By Sergey N. Dorogovtsev, José Fernando Ferreira Mendes. 2000

205 citations recorded by the source corpus.

We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barabási and Albert in the particular case of growing networks. The networks considered here evolve according to the following rules: i) Each instant a new site is added, the probability of its connection to old sites is proportional to their connectivities. ii) In addition, a) new links between some old sites appear with probability proportional to the product of their connectivities or b) some links between old sites are removed with equal probability.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c0007e20ac8ec2da1aa174f0f556635b796aa50c

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In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

A Survey of Statistical Network Models (2009, background): “For example, Dorogovtsev and Mendes [90] proposed that creating an edge to node i should be proportional not just to its degree ki but also to its age, decaying as (t − ti)−ν , where ν is a tunable parameter.”
Structure of growing social networks. (2001, background): “) Other features, such as removal of vertices or edges, or movement of edges to new positions in the network, can also be incorporated [18], but the crucial features of power-law degree distributions and correlations between vertex degrees are reproduced with only the elements 1 and 2 above.”
Trees, networks, and hydrology (2006, background): “…can be mathematically described by networks of interacting elements, and loops are ubiquitous [e.g., Bollobas, 2001; Barabási and Albert, 1999; Albert and Barabási, 2002; Barabási et al., 2000, 2002; Montoya and Solé, 2002; Dorogovtsev and Mendes, 2000, 2002; Newman, 2003; Song et al., 2005].”
Evolution of networks (2001, background): “4,132,135,139,143–147]. Here, we discuss the opposite situation, part oflinks maydisappear during the network growth. This situation, an additional permanent deletion of links, is considered in Refs. [85,138,139]. Here we write down the result for the typical case of the model of Sec. VIIIE in which”
Statistical mechanics of complex networks (2001, background): “Dorogovtsev and Mendes (2000c) consider a class of undirected models in which new edges are added between old sites and existing edges can be removed.”
The Structure and Function of Complex Networks (2003, methodology): “Of particular note is the work by Dorogovtsev and Mendes [114, 116] and by Krapivsky and Redner [246].”