Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
random graph model
|
| gptkbp:application |
gptkb:percolation_theory
computer science social network analysis epidemic modeling modeling random networks |
| gptkbp:describes |
random graphs with n vertices
|
| gptkbp:edgeCount |
M
|
| gptkbp:edgeProbability |
p
|
| gptkbp:field |
gptkb:probability_theory
graph theory |
| gptkbp:G(n,_M) |
graph with n vertices and M edges chosen uniformly at random
|
| gptkbp:G(n,_p) |
graph with n vertices, each edge included independently with probability p
|
| gptkbp:hasDegreeDistribution |
Poisson (in large n limit)
binomial |
| gptkbp:hasLimitingBehavior |
appearance of cycles
emergence of connected component giant component appears at p = 1/n graph becomes connected at p = (log n)/n |
| gptkbp:hasModel |
G(n, M)
G(n, p) |
| gptkbp:hasNoMultipleEdges |
true
|
| gptkbp:hasNoSelfLoops |
true
|
| https://www.w3.org/2000/01/rdf-schema#label |
Erdős–Rényi random graph
|
| gptkbp:introducedIn |
1959
|
| gptkbp:isSimpleGraph |
true
|
| gptkbp:isUndirected |
true
|
| gptkbp:isUnweighted |
true
|
| gptkbp:namedAfter |
gptkb:Paul_Erdős
gptkb:Alfréd_Rényi |
| gptkbp:parameter |
M
n p |
| gptkbp:property |
phase transition
Poisson degree distribution giant component threshold functions |
| gptkbp:publishedIn |
gptkb:On_Random_Graphs_I
gptkb:On_the_Evolution_of_Random_Graphs |
| gptkbp:relatedTo |
gptkb:Barabási–Albert_model
gptkb:Gilbert_random_graph random regular graph small-world network |
| gptkbp:usedIn |
combinatorics
statistical physics network science |
| gptkbp:vertices |
n
|
| gptkbp:bfsParent |
gptkb:Paul_Erdős
|
| gptkbp:bfsLayer |
4
|