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Results tagged with random-graphs
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user 1131
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
2
votes
Accepted
The expected value of common neighbors on a random regular graph
Yep, it is $\frac{d(d-1)}{n-1}$ in general. Fix a $d$-regular graph and average over the action of the permutation group on the vertices. We are interested in the event $S(x,y,z)=$"$x$ is connected to …
- 61.9k
8
votes
Accepted
Probability of the random graph on $2n$ vertices having exactly $n$ vertices with degree $\g...
It certainly tends to $0$. The way to see it almost without any computation is to mark any $n$ disjoint edges. Then, when deciding the fate of the remaining edges, each vertex has $p=2^{2-2n}{2n-2\cho …
- 61.9k
3
votes
Nearest neighbors on random complete graph
Not sure about the reference, but the "probability proof" is already nearly trivial.
Just notice that you can run your assignment step by step, at each step either placing some particular weighted edg …
- 61.9k
7
votes
What nodes of a graph should be vaccinated first?
I took a look at a very simple model: SIR for 2 population groups with the interaction matrix $A=\begin{bmatrix}\alpha & \lambda\\\mu & \beta\end{bmatrix}$, which, roughly speaking, corresponds to the …
- 61.9k