Deterministic scale-free networks

By Albert-László Barabási, E. Ravasz, Tamás Vicsek. 2001

439 citations recorded by the source corpus.

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are stochastic, that is they create networks in which the nodes appear to be randomly connected to each other. Here we propose a simple model that generates scale-free networks in a deterministic fashion. We solve exactly the model, showing that the tail of the degree distribution follows a power law.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/353f90472ad4f3d58fa97e5bb89414bd01e5cab4

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In Geometry and Topology

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Citations in the corpus

Kronecker Graphs: An Approach to Modeling Networks (2008, methodology): “This is a property that requires some care in order to gt right, as standard recursive constructions (for example, the traditional Cartesian product or the construction of (Barabási et al., 2001)) do not yield graphs satisfying the densification power law.”
Realistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication (2005, background): “This is a property that requires some care in order to get right, as standard recursive constructions (for example, the traditional Cartesian product or the construction of [4]) do not satisfy it.”
Bipartite Graphs as Models of Complex Networks (2003, positive): “Some deterministic models, which we do not detail here, have also been introduced [8, 22] which produce the wanted properties and are suitable for analysis.”
Random walks and diffusion on networks (2016, neutral): “(51) 10”
Critical phenomena in complex networks (2007, methodology): “Note that if multiple connections are allowed, this construction is essentially equivalent to the simple balls-inboxes (or backgammon) model (Bialas et al., 2000, 1997), where ends of edges—balls—are statistically distributed among vertices—boxes.”
Indicators for Complex Innovation Systems (2006, background): “Sometimes the intercept of a power law is used as an indicator, particularly in physical systems.”