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Rado graph

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…

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Rado graph

Nodes104
Edges103
Triples132
Avg. degree1.98
Density0.019231
Components1

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Rado graph

Top relations

related to Other constructions · 12
Rado graph → Ackermann, Ackermann's, BIT, By, In, One, Paley, Rado, Skolem's, The Rado, There, This
related to Extension · 11
Rado graph → Because, Chinese, Dirichlet's, For, However, Paley, Rado, The Rado, Then, Thus, With
related to Finite graphs and computational complexity · 11
Rado graph → As Fagin, Based, Because, Fagin's, For, However, It, PSPACE-complete, Rado, Symmetrically, This
related to Partitions · 11
Rado graph → Bonato, But, Cameron, Delić, Diestel, For, However, More, Rado, Ramsey, This
related to history · 10
Rado graph → Ackermann, Ackermann's, Erdős, Rado, Rado's, RichardRado, Rényi, Strictly, The Rado, They
related to Completeness · 9
Rado graph → Because, Gaifman, Gaifman's, In, Rado, The, Therefore, This, Vaught
related to Random graph · 9
Rado graph → Erdős, PaulErdősandAlfréd Rényi, Rado, Repeatedly, Rényi, Specifically, The Rado, This, With
related to Binary numbers · 8
Rado graph → Ackermann, An, BIT, Rado, The, They, Thus, Vertex
is a · 7
Rado graph → corresponding undirected graph given by forgetting the directions on the edges, example of the unique countable model of an ω-categorical theory, prototypical example of a theory with the independence property, self-complementary graph, self-complementary graph.Other constructionsIn one of Ackermann's original 1937 constructions, symmetric graph.The automorphism group of the Rado graph is a simple group, unique countable graph with the extension property implies that it is also the unique countable model for its theory
related to Induced subgraphs · 7
Rado graph → Adding, At, By, Rado, The, This, To

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Important terminology

graph rado displaystyle finite vertices graphs one property extension vertex induced theory infinite isomorphic sets two subgraphs random every also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Rado graphis aexample of the unique countable model of an ω-categorical theory0.90text
Rado graphis acorresponding undirected graph given by forgetting the directions on the edges0.90text
Rado graphis aself-complementary graph.Other constructionsIn one of Ackermann's original 1937 constructions0.90text
Rado graphis aself-complementary graph0.90text
Rado graphis asymmetric graph.The automorphism group of the Rado graph is a simple group0.90text
Rado graphis aunique countable graph with the extension property implies that it is also the unique countable model for its theory0.90text
Rado graphis aprototypical example of a theory with the independence property0.90text
Rado graphrelated to Binary numbersAckermann0.60section
Rado graphrelated to Binary numbersRado0.60section
Rado graphrelated to Binary numbersBIT0.60section
Rado graphrelated to Binary numbersThey0.60section
Rado graphrelated to Binary numbersAn0.60section

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