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gptkbp:instanceOf
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gptkb:random_graph_model
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gptkbp:application
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gptkb:percolation_theory
computer science
social network analysis
epidemic modeling
modeling random networks
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gptkbp:describes
|
random graphs with n vertices
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gptkbp:edgeCount
|
M
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gptkbp:edgeProbability
|
p
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gptkbp:field
|
gptkb:probability_theory
graph theory
|
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gptkbp:G(n,_M)
|
graph with n vertices and M edges chosen uniformly at random
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gptkbp:G(n,_p)
|
graph with n vertices, each edge included independently with probability p
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|
gptkbp:hasDegreeDistribution
|
Poisson (in large n limit)
binomial
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|
gptkbp:hasLimitingBehavior
|
appearance of cycles
emergence of connected component
giant component appears at p = 1/n
graph becomes connected at p = (log n)/n
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|
gptkbp:hasModel
|
G(n, M)
G(n, p)
|
|
gptkbp:hasNoMultipleEdges
|
true
|
|
gptkbp:hasNoSelfLoops
|
true
|
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gptkbp:introducedIn
|
1959
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gptkbp:isSimpleGraph
|
true
|
|
gptkbp:isUndirected
|
true
|
|
gptkbp:isUnweighted
|
true
|
|
gptkbp:namedAfter
|
gptkb:Paul_Erdős
gptkb:Alfréd_Rényi
|
|
gptkbp:parameter
|
M
n
p
|
|
gptkbp:property
|
gptkb:phase_transition
Poisson degree distribution
giant component
threshold functions
|
|
gptkbp:publishedIn
|
gptkb:On_Random_Graphs_I
gptkb:On_the_Evolution_of_Random_Graphs
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gptkbp:relatedTo
|
gptkb:Barabási–Albert_model
gptkb:Gilbert_random_graph
random regular graph
small-world network
|
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gptkbp:usedIn
|
gptkb:combinatorics
statistical physics
network science
|
|
gptkbp:vertices
|
n
|
|
gptkbp:bfsParent
|
gptkb:Paul_Erdős
|
|
gptkbp:bfsLayer
|
5
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Erdős–Rényi random graph
|