The degree sequence of a scale‐free random graph process

By Béla Bollobás, Oliver Riordan, Joel H. Spencer, Gábor E. Tusnády. Random Struct. Algorithms, 2001

830 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ed88723f30a8f8d2928412a7a1215a488b5ef042

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On compressing social networks (2009, methodology): “Also, we remove all nodes of degree > k, for some constant k — by [9] only kn edges and nodes will be removed this way.”
Growth of preferential attachment random graphs via continuous-time branching processes (2007, background): “1) in terms of an embedding in continuous-time branching processes which allows for extensions of law of large numbers and maximal degree growth asymptotics, first approached by difference equations and martingale methods, in [8], [10], [13], [14].”
Why rumors spread so quickly in social networks (2012, methodology): “Famous structural results prove small diameters for such graphs, 10 determine their degree (in terms of number of neighbors) distribution, 11 and show high expansion properties 24 and robustness against random damage, along with vulnerability against malicious attacks.”
The Structure and Function of Complex Networks (2003, background): “69) In the limit of large k this gives a power law degree distribution pk ∼ k−3, with only the single ﬁxed exponent α = 3. A more rigorous derivation of this result has been given by Bollob´as et al. [65]. 31 The behavior of the model at ﬁnite system sizes has been investigated by Krapivsky and Redn”
A survey of random processes with reinforcement (2006, background): “iscussion in their Section 3.2 of the perils of unjustiﬁed heuristics with regard to this model). The only published, rigorous analysis of preferential attachment that I know of is by Bollobas et al. [BRST01] and is restricted to the case α = 0. Bollobas et al. clean up the deﬁnition of G0,m n with ”
Degree asymptotics with rates for preferential attachment random graphs (2011, background): “Model 2 is one studied in Bollobás et al. (2001) and allows for self-connecting edges.”
An almost-bijective proof of an asymptotic property of partitions (2007, background): “In [4] and [11] the authors derive the asymptotic degree distribution for a model that is equivalent to the special case, when the weight function is linear.”
Fundamentals of Stein's method (2011, result): “We prove the following geometric approximation result (convergence was shown without rate in [15]), which is weaker than the result of [42] but has a slightly simpler proof.”
Random Graphs and Complex Networks (2016, methodology): “The first to investigate the model rigorously, were Bollobás, Riordan, Spencer and Tusnady [48].”
Graph theory and networks in Biology. (2006, neutral): “In this subsection, we shall discuss four classical concepts of centrality which have recently been applied to biological interaction networks: (i) Degree centrality; (ii) Closeness centrality; (iii) Betweenness centrality; (iv) Eigenvector centrality.”
Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet (2002, background): “In other words, we do not pursue here sharp convergence results à la [8,4,1], content to bound the distribution away from exponential ones.”