 Linearized chord diagram model

Start with one self-loop, and at step $t$ add one vertex and one edge. An old vertex $i$ is chosen with probability $d_i(t-1)/(2t-1)$, and the new vertex is chosen with probability $1/(2t-1)$, producing a self-loop. Self-loops contribute two to the degree of a vertex. There are $n$ edges and total vertex degree $2n$ at time $n$. This exact normalization is distinct from treating the total vertex degree as the number of edges.