# Erdos-Renyi conditioned on node degrees

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.

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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