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In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge. The names of this graph honor Richard Rado, Paul Erdős, and Alfréd Rényi, mathematicians who studied it in the early 1960s; it appears even earlier in the work of Wilhelm Ackermann. The Rado graph can also be constructed non-randomly, by symmetrizing the membership relation of the hereditarily finite sets, by applying the BIT predicate to the binary representations of the natural numbers, or as an infinite Paley graph that has edges connecting pairs of prime numbers congruent to 1 mod 4 that are quadratic resid

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Communication100033020 yago:Graph107000195 yago:WikicatIndividualGraphs yago:WikicatInfiniteGraphs yago:VisualCommunication106873252 yago:WikicatRandomGraphs
rdfs:label	Rado-Graph (de) Graphe de Rado (fr) 라도 그래프 (ko) Rado graph (en) Граф Радо (ru) Граф Радо (uk)
rdfs:comment	Der Rado-Graph (auch als Erdős-Rényi-Graph oder Zufallsgraph bezeichnet) ist ein spezieller abzählbar unendlicher Graph, der fast sicher entsteht, wenn jedes Knotenpaar unabhängig und mit Wahrscheinlichkeit durch eine Kante verbunden wird. Eine wichtige Erkenntnis ist, dass ein Satz in der Prädikatenlogik erster Stufe genau dann für fast alle endlichen Graphen gilt, wenn vom Rado-Graphen erfüllt wird. Er ist aufgrund von Arbeiten in den 1960er-Jahren nach Richard Rado bzw. Rado, Paul Erdős und Alfréd Rényi benannt, taucht aber schon 1937 bei Wilhelm Ackermann auf. (de) En mathématiques, et plus précisément en théorie des graphes, le graphe de Rado, appelé également graphe d'Erdős–Rényi ou graphe aléatoire, est un graphe infini dénombrable étudié au début des années 1960 par Richard Rado, Paul Erdős et Alfréd Rényi, caractérisé par la , qui implique qu’il contient (en tant que sous-graphe) n'importe quel graphe fini ou dénombrable. Il en existe plusieurs constructions ; c'est en particulier (presque sûrement) le graphe aléatoire obtenu en choisissant au hasard pour chaque paire de sommets s'ils sont connectés ou non. (fr) 그래프 이론에서 라도 그래프(영어: Rado graph)는 사실상 유일한 가산 무한 무작위 그래프이다. (ko) Граф Радо — єдиний (з точністю до ізоморфізму) зліченний граф R, такий, що для будь-якого скінченного графу G і його вершини v будь-яке вкладення G − v в R як породженого підграфу можна розширити до вкладення G в R. Як наслідок, граф Радо містить усі скінченні і зліченні нескінченні графи як підграфи. Граф Радо відомий також під назвами випадковий граф і граф Ердеша — Реньї. (uk) Граф Радо — единственный (с точностью до изоморфизма) счётный граф R, такой, что для любого конечного графа G и его вершины v любое вложение G − v в R в качестве порождённого подграфа может быть расширено до вложения G в R. Как результат граф Радо содержит все конечные и счётные бесконечные графы в качестве подграфов.Граф Радо известен также под именами случайный граф и граф Эрдёша — Реньи. (ru) In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge. The names of this graph honor Richard Rado, Paul Erdős, and Alfréd Rényi, mathematicians who studied it in the early 1960s; it appears even earlier in the work of Wilhelm Ackermann. The Rado graph can also be constructed non-randomly, by symmetrizing the membership relation of the hereditarily finite sets, by applying the BIT predicate to the binary representations of the natural numbers, or as an infinite Paley graph that has edges connecting pairs of prime numbers congruent to 1 mod 4 that are quadratic resid (en)
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dcterms:subject	Individual graphs Infinite graphs Random graphs
Wikipage page ID	7785594 (xsd:integer)
Wikipage revision ID	1111229963 (xsd:integer)
Link from a Wikipage to another Wikipage	Cardinality of the continuum Model theory Omega-categorical theory Universal quantification Binary numeral system Binary sequence Definite article Almost surely Paul Erdős Richard Rado Robert Lawson Vaught Indagationes Mathematicae Index of a subgroup Induced subgraph PSPACE-complete Isolated vertex Zero–one law Individual graphs Complete graph Countable set Countably infinite Matching (graph theory) Mathematics Simple group Quadratic residue Łoś–Vaught test Fraïssé limit Continuum hypothesis Infinite graphs Erdős–Rényi model Logic of graphs Clique (graph theory) Combinatorica Compactness theorem Complement graph Complete theory Mathematische Annalen Subgroup Mathematical Proceedings of the Cambridge Philosophical Society Acta Mathematica Hungarica Random graphs Morley's categoricity theorem Absolute value Aleph number Alfréd Rényi Almost all Edge coloring European Congress of Mathematics First-order logic Forcing (mathematics) Cardinality Diameter (graph theory) Directed graph Dirichlet's theorem on arithmetic progressions Graph automorphism Graph isomorphism Graph theory Israel Journal of Mathematics Logical connective Predicate (mathematical logic) Quadratic reciprocity Hamiltonian path Intersection graph Isometry Back-and-forth method Prime number Chinese remainder theorem Jerzy Łoś Block design Symmetric graph Symmetric relation Henson graph Hereditarily finite set Homogeneous graph

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