Mathematical results on scale‐free random graphs

By Béla Bollobás, Oliver Riordan. 2005

548 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/99897e09ca03dcd26a3acbb9fc8c5287ccc10cce

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In Computational Theory and Mathematics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

The phase transition in inhomogeneous random graphs (2005, background): “], Buckley and Osthus [29] and 4 BELA BOLLOB´ AS, SVANTE JANSON, AND OLIVER RIORDAN´ Cooper and Frieze [40]. For a partial survey of the rapidly growing body of rigorous work see Bollobas and Riordan [21]. Needless to say, surveys in an active area such as this quickly become dated, and there are al”
Statistical properties of community structure in large social and information networks (2008, background): “Finally, we also compare results with analytical and/or simulational results on a wide range of commonly and not-so-commonly used network generation models [124, 25, 9, 101, 135, 111, 70, 71].”
Extremal Properties of Random Structures (2003, unknown): “[ 4 ] Sect. 11) to produce power law distributions for indegree.”
Random Graphs and Complex Networks (2016, methodology): “The explicit limiting distribution of maxiDi(t)/(2m √ t) was proved by Bollobás and Riordan in [53].”
Random graphs (2006, methodology): “There is a simple iterative algorithm to check whether a sequence is graphical.”
On compressing social networks (2009, background): “The well-known preferential attachment (PA) model [2, 8], for instance, generates graphs in this class.”
Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters (2008, background): “There has been a large body of work subsequent to that of Albert and Barabási [9] on models in which edges are added via a preferential-attachment or rich-gets-richer mechanism [127, 25].”
Aggregate Fluctuations and the Network Structure of Intersectoral Trade (2010, methodology): “These are a 18The classical binomial model of Erdos and Renyi (see Bollobas (2001) for a texbook treatment) is the most commonly used construction for random graphs but there are many alternatives to this (see Durret, 2006, Newman, 2003, Bollobas and Riordan, 2003, or Chung and Lu, 2006 ).”
Main-memory triangle computations for very large (sparse (power-law)) graphs (2008, background): “1 Even though some authors make no distinction between the two notions, they are different, see for instance [12,32].”
The internet AS-level topology: three data sources and one definitive metric (2005, background): “cient Ccoeff , which is the percentage of 3-cycles among all connected node triplets in the entire graph (for the exact definition, see [30]).”
Spectra of Large Random Trees (2009, background): “We refer the reader to [7, 15, 23] for relevant references.”
Asymptotic behavior and distributional limits of preferential attachment graphs (2014, background): “Since these works there has been a tremendous amount of study, both nonrigorous and rigorous, of the random graph models that explain the power-law degree distribution; see [1] and [9] and references therein for some of the nonrigorous and rigorous work, respectively.”