Erdős–Rényi model
E204641
The Erdős–Rényi model is a fundamental random graph model in probability theory and network science, where edges between pairs of nodes are included independently with a fixed probability.
All labels observed (8)
| Label | Occurrences |
|---|---|
| Erdős–Rényi random graph | 2 |
| Erdős–Rényi model canonical | 1 |
| Erdős–Rényi model of random graphs | 1 |
| G(n,M) model | 1 |
| G(n,p) model | 1 |
| Gilbert model | 1 |
| On Random Graphs I | 1 |
| binomial random graph | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1819301 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Erdős–Rényi model Context triple: [Alfréd Rényi, knownFor, Erdős–Rényi model]
-
A.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
-
B.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
C.
Goodman–Martínez–Thompson correlation
The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
-
D.
Monte Carlo
Monte Carlo is a famous district of Monaco renowned for its luxury casinos, upscale resorts, and role as a glamorous hub for high-end tourism and events like the Monaco Grand Prix.
-
E.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Erdős–Rényi model Target entity description: The Erdős–Rényi model is a fundamental random graph model in probability theory and network science, where edges between pairs of nodes are included independently with a fixed probability.
-
A.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
-
B.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
C.
Goodman–Martínez–Thompson correlation
The Goodman–Martínez–Thompson correlation is the most widely accepted scholarly conversion formula that aligns dates in the ancient Maya Long Count calendar with the Gregorian calendar.
-
D.
Monte Carlo
Monte Carlo is a famous district of Monaco renowned for its luxury casinos, upscale resorts, and role as a glamorous hub for high-end tourism and events like the Monaco Grand Prix.
-
E.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical model
ⓘ
network science concept ⓘ probability theory concept ⓘ random graph model ⓘ |
| alsoKnownAs |
Bernoulli random graph
ⓘ
Erdős–Rényi model ⓘ
surface form:
Erdős–Rényi random graph
Erdős–Rényi model ⓘ
surface form:
binomial random graph
|
| assumes |
fixed edge probability
ⓘ
independent edges ⓘ no multiple edges ⓘ no self-loops ⓘ |
| asymptoticDegreeDistribution | Poisson distribution for sparse regime ⓘ |
| averagePathLength | O(log n) ⓘ |
| category | random graphs ⓘ |
| clusteringCoefficient | approximately equal to p ⓘ |
| connectivityThreshold | p ≈ (log n)/n ⓘ |
| describes | random graphs ⓘ |
| edgeCountDistributionInG(n,p) | binomial with parameters (n choose 2) and p ⓘ |
| edgeInclusion | independent for each unordered pair of vertices ⓘ |
| edgeProbability | p ⓘ |
| field |
graph theory
ⓘ
network science ⓘ probability theory ⓘ |
| formalizedIn |
Erdős–Rényi model
self-linksurface differs
ⓘ
surface form:
On Random Graphs I
|
| giantComponentThreshold | p ≈ 1/n ⓘ |
| hasProperty |
edges are identically distributed
ⓘ
edges are independent ⓘ graph is simple ⓘ graph is undirected ⓘ |
| hasVariant |
Erdős–Rényi model
self-linksurface differs
ⓘ
surface form:
G(n,M) model
Erdős–Rényi model self-linksurface differs ⓘ
surface form:
G(n,p) model
|
| influenced | modern network science ⓘ |
| introducedBy |
Alfréd Rényi
ⓘ
Pál Erdős ⓘ
surface form:
Paul Erdős
|
| introducedIn | 1959 ⓘ |
| namedAfter |
Alfréd Rényi
ⓘ
Pál Erdős ⓘ
surface form:
Paul Erdős
|
| probabilitySpace | set of all simple graphs on n labeled vertices ⓘ |
| relatedTo |
Erdős–Rényi model
self-linksurface differs
ⓘ
surface form:
Gilbert model
|
| studiedIn |
combinatorics
ⓘ
computer science ⓘ statistical physics ⓘ |
| typicalDegreeDistribution | binomial distribution ⓘ |
| usedFor |
benchmarking network algorithms
ⓘ
studying connectivity thresholds ⓘ studying degree distributions ⓘ studying giant component emergence ⓘ studying phase transitions in graphs ⓘ |
| vertexCountParameter | n ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Erdős–Rényi model Description of subject: The Erdős–Rényi model is a fundamental random graph model in probability theory and network science, where edges between pairs of nodes are included independently with a fixed probability.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Erdős–Rényi random graph
this entity surface form:
Erdős–Rényi model of random graphs
this entity surface form:
G(n,p) model
this entity surface form:
G(n,M) model
this entity surface form:
Erdős–Rényi random graph
this entity surface form:
binomial random graph
this entity surface form:
On Random Graphs I
this entity surface form:
Gilbert model