Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Has anyone worked out what the distribution of an Erdos-Renyi graph/adjacency matrix is conditioned on the degree sequence of the graph?

More precisely, if $A$ is the adjacency matrix of $G(n,p)$, that is $A_{ij} \sim \text{Bernoulli}(p)$ for $ 1 \le i \le j \le n$, $A$ is symmetric, and we let $d_i = \sum_j A_{ij}$, what is the distribution of $A$ given $(d_1,\dots,d_n)$? Any references is appreciated.

share|cite|improve this question
Conditioned on $(d_1,\dots,d_n)$, $G$ is a random graph uniformly distributed in the set of graphs with degree sequence $(d_1,\dots,d_n)$. – Yury Dec 14 '12 at 15:29
Thanks. Seems you are right. – passerby51 Dec 20 '12 at 1:25

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.