Skip to main content
1 of 2
Manfred Weis
  • 13.2k
  • 4
  • 34
  • 76

Probability of a vertex being a "degree-celebrity" in a random graph

If $G(n,p)$ is a random graph of the Erdös-Rényi model,
what is the probability that $\mathrm{deg}(v)\gt\mathrm{deg}(u)\ \forall u\in\mathrm{adj}(v)$

Please feel free to relate answers to other models of random graphs.

Manfred Weis
  • 13.2k
  • 4
  • 34
  • 76