TABLE I.

Expected edge strength for several different types of random networks.

Null model	Expected edge strength
Expected Bernoulli random network conditioned on degrees of associated nodes.	$E(A_{ij}\mid k_i,k_j)=\{\begin{array}{ll}\frac{k_i{k}_j}{k_i{k}_j+(N-1-k_i)(N-1-k_j)·(p/(1-p))},\hfill & i\ne j\hfill \\ 0,\hfill & i=j\hfill \end{array}$
Expected Gaussian random network conditioned on degrees of associated nodes.	$E(A_{ij}\mid k_i,k_j)=\{\begin{array}{ll}\frac{k_i+k_j-(N-2)\mu }{N},\hfill & i\ne j\hfill \\ 0,\hfill & i=j\hfill \end{array}$
Expected Gaussian random network conditioned on whole degree sequence. Also, BLUE null model in the non-Gaussian case.	$E(\mathbf{x}\mid \mathbf{Hx}=\mathbf{k})={\mathit{\mu }}_{\mathbf{x}}+{\mathrm{\sum }}_{\mathbf{xk}}{\mathrm{\sum }}_{\mathbf{k}}^{-1}(\mathbf{k}-{\mathit{\mu }}_{\mathbf{k}})$
Expected i.i.d. Gaussian random network conditioned on whole degree sequence.	$E(A_{ij}\mid \mathbf{k})=\{\begin{array}{ll}\frac{k_i+k_j}{N-2}-\frac{2m}{(N-1)(N-2)},\hfill & i\ne j\hfill \\ 0,\hfill & i=j\hfill \end{array}$