Topology of evolving networks: local events and universality

By Réka Albert, Albert-László Barabási. Physical Review Letters, 2000

1,336 citations recorded by the source corpus.

Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can emerge, the connectivity distribution following either a generalized power law or an exponential. We propose a continuum theory that predicts these two regimes as well as the scaling function and the exponents, in good agreement with numerical results. Finally, we use the obtained predictions to fit the connectivity distribution of the network describing the professional links between movie actors.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9f0b94924f88f876baf985b88c1ca4e5b86c6563

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Citations in the corpus

Patterns and dynamics of users' behavior and interaction: Network analysis of an online community (2009, background): “In agreement with recent theoretical and empirical studies of network growth (Albert & Barabási, 2000; Barabási et al., 2002; Guimerà, Uzzi, Spiro, Amaral, 2005), the community thus evolves as a result of not only the contributions of newcomers but also the continuing activities of incumbents.”
A General Framework for Weighted Gene Co-Expression Network Analysis (2005, neutral): “, 2004) The emergence of power-law distribution (scale free topology) is intimately linked to the growth of the network in which new nodes are preferentially attached to already established nodes, a property that is also thought to characterize the evolution of biological systems (Barabasi and Alber”
Random geometric graphs. (2002, background): “Properties of real networks like robustness [16, 17], growth [11, 18, 19, 20], and topology have attracted much attention, primarily from physicists.”
The Structure and Function of Complex Networks (2003, background): “Then in Section VII we look at models of growing networks, particularly the models of Price [344] and Barabási and Albert [32], and generalizations.”
Evolution of networks (2001, background): “D (1982±June 1997) [100]; 5a is the ® exponent for the collaboration network of movie actors [55]; 5a 0 is the result of another ®tting for the same data [102]; 5b is ® for the collaboration network of Medline [13]; 5b 0 is ® for the collaboration net collected from mathematical journals [15]; 5b 00”
Network Structure, Self-Organization and the Growth of International Collaboration in Science.Research Policy, 34(10), 2005, 1608-1618. (2005, result): “In findings similar to others (Barabási & Albert 1999; Albert & Barabási 2000; Barabási et al 2002) the networks of collaborations shown in the figures below have fat tailed degree distributions.”