= Configuration model
{wiki}
= Pairing model
{synonym}
For a prescribed <degree sequence> with even sum $M=\sum_i d_i$, attach $d_i$ labelled <half-edges> to <vertex> $i$ and choose a uniform <perfect matching> of the $M$ half-edges. Each pair becomes an <edge>, giving a <multigraph> that may have <self-loops> or parallel edges. The number of pairings is $M!/[2^{M/2}(M/2)!]$. Every <simple graph> with that degree sequence has exactly $\prod_i d_i!$ pairing representations, so conditioning on simplicity produces the uniform simple-graph model.
Back to article page
