Algorithm 5.

procedure AddEdge

	Input: individual v, layer j.
1	// Determine candidate new neighbors for v.
2	$C_j^t\left(v\right)≔V_j^t\backslash (N_j^t\left(v\right)\cup \left\{v\right\})$.
3	if $\mid C_j^t\left(v\right)\mid >0$ then
4	foreach c in $C_j^t\left(v\right)$ do
5	Compute the bias due to degree constraints:
	$a_{\delta }^t\left(c\right)≔\{\begin{array}{cc}{e}^{-1∕(d_j\left(v\right)-\mid N_j^t\left(v\right)\mid )}\hfill & \mid N_j^t\left(u\right)\mid <d_j\left(u\right)\hfill \\ 0\hfill & \text{otherwise}.\hfill \end{array}\phantom{\}}$
6	Compute the bias due to the bivariate degree distribution:
	$a_{\chi }^t(v,c)≔\stackrel{=}{{\chi }_j}(\mid N_j^t\left(v\right)\mid -∊,\mid N_j^t\left(v\right)\mid +∊,\mid N_j^t\left(c\right)\mid -∊,\mid N_j^t\left(c\right)\mid +∊)$.
7	Compute the bias due to bivariate attribute distributions:
	$a_{\beta }^t\left(c\right)≔{\prod }_{i=1}^m{\beta }_{i,j}(x_i\left(v\right),x_i\left(c\right))$.
8	Compute the bias due to triadic closures:
	$a_{\Delta }^t\left(c\right)≔\zeta (w_j^{\Delta }-1)\cdot {\Delta }_j^t(v,c)$
	where ${\Delta }_j^t(v,c)=\#$ layer j triangles formed on adding layer j edge (v, c).
9	Compute propensity of edge (v, c) as the product of 4 biases:
	$w_j^t\left(c\right)≔a_{\delta }^t\left(c\right)\cdot a_{\chi }^t\left(c\right)\cdot a_{\alpha }^t\left(c\right)\cdot a_{\Delta }^t\left(c\right)$.
10	Normalize propensity to obtain a distribution over $C_j^t\left(v\right):$:
	$p_j^t\left(c\right)≔\frac{{\omega }_j^t\left(c\right)}{{\sum }_{c^{\prime }\in C_j^t\left(v\right)}{\omega }_j^t\left(c^{\prime }\right)}$.
11	w := choose from $C_j^t\left(v\right)$ randomly according to distribution $p_j^t$.
12	// Add the layer j edge connecting v to w.
13	$N_j^t\left(v\right)≔N_j^t\left(v\right)\cup \left\{(v,w)\right\}$