What is the probability that a random graph G(n,p) with n nodes and probability p = c some constant value is complete?
By complete I mean that every pair of nodes is connected by an edge. Check this for further details.
2026-03-28 14:25:42.1774707942
Probability of having a complete random graph
756 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROBABILITY
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Prove or disprove the following inequality
- Another application of the Central Limit Theorem
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$
- proving Kochen-Stone lemma...
- Solution Check. (Probability)
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
Related Questions in GRAPH-THEORY
- characterisation of $2$-connected graphs with no even cycles
- Explanation for the static degree sort algorithm of Deo et al.
- A certain partition of 28
- decomposing a graph in connected components
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Fake induction, can't find flaw, every graph with zero edges is connected
- Triangle-free graph where every pair of nonadjacent vertices has exactly two common neighbors
- Inequality on degrees implies perfect matching
- Proving that no two teams in a tournament win same number of games
- Proving that we can divide a graph to two graphs which induced subgraph is connected on vertices of each one
Related Questions in RANDOM-GRAPHS
- Bound degrees of sparse random graphs
- Connectivity of random graphs - proof $\frac{logn}{n}$ is threshold
- In weighed random graph where the edge weight is restricted to $[0,1]$, what are the usual assumptions of edge weight distribution?
- Upper Bound on Vertices in SCC Graph of Directed Random Graph
- The degree of a vertex in $G(n,m)$ is approx. Poisson
- What is the expected length of the diameter of a special random graph?
- Clique numbers and Theorem 4.5.1 in "The Probabilistic Method" by Alon and Spencer
- Expected global clustering coefficient for Erdős–Rényi graph
- Probability of having a path of a given length in a random graph?
- Correlation for random graph (Erdos-Renyi)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
By your notation, I'm assuming that $p$ is the probability for the existence of an edge between any two nodes. Then you can think of the generation of a random graph as a series of ${n\choose2}$ Bernoulli trials, one for each possible edge, with probability $p$ of success in each trial. The probability that they are all successes, and so resulting in a complete graph, is $p^{n\choose2}$.