On the Evolution of Random Graphs

By P. Erd6s, A. R~nyi

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In Algorithms & Complexity

Citations in the corpus

Bayesian Structure Learning with Generative Flow Networks (2022, methodology): “Therefore, we sampled N = 100 datapoints from a randomly generated (under an Erd˝os-Rényi model; Erd˝os and Rényi, 1960) We evaluated the quality of the approximation based on the probability of various structural features.”
Statistical physics of vaccination (2016, unknown): “lattices, small-world networks (SW) [174, 505], Erdös-Rényi random graphs (ER) [506], and Barabási-Albert scale-free networks (BA or SF) [507].”
The phase transition in inhomogeneous random graphs (2005, background): “Then c 0 ρ ′ + (c 0 ) ≤ 2, with equality in the classical Erd˝ os–Rényi case.”
Agreement over random networks (2004, methodology): “In this note, we will not consider these more general models and instead, enjoy the elegance offered by the random graph model as proposed by Erdős and Rényi [5].”
Critical random graphs: Diameter and mixing time (2007, unknown): “2 and the following fact, first proved in [10] (see also [1], [18] and [21]): In G(n, 1+λn −1/3 n ), lim inf n P(|C1| > βn) → 1 , as β → 0 .”
The component sizes of a critical random graph with given degree sequence (2010, background): “Then, for large integers n, SGn is an approximation of the Erdős–Renyi random graph G(n,1/n).”
An Energy-Balanced Routing Method Based on Forward-Aware Factor for Wireless Sensor Networks (2014, methodology): “In [17], Erdös and Rényi propose ER random graph model based on classic graph theory and statistical physics.”
Analysis of global control of Escherichia coli carbohydrate uptake (2007, unknown): “This network can be interpreted as the expected adjacency matrix of an Erdös-Rényi network [37].”
The topology of the transcription regulatory network in the yeast (2002, methodology): “The test graphs include an uncorrelated random graph [9], a small-world graph [10], and a scale-free graph [11], representing the three major network families known in graph theory [12].”