Algorithm 1 Matrix scaling and consensus (collective)

1:init $x\left(0\right)$ 2:$L=D_A^{out}-A$ 3:$\Delta \left(0\right)=D_L^{-1}$ 4:$\overline{P}=(I-\Delta \left(0\right)\ast L)$ 5:$P\left(0\right)=\overline{P}\Delta \left(0\right)+[I-\Delta \left(0\right)]$ 6:$\pi \left(0\right)=\mathbf{0},\eta \left(0\right)=\mathbf{1}$ 7:repeat 8: $\pi (t+1)=P\left(0\right)\pi \left(t\right)$ 9: $\eta (t+1)=max\left(\pi \left(t\right),max\eta \left(t\right)A\right)$ 10: $\Delta (t+1)=\Delta \left(0\right)\frac{\pi (t+1)}{\eta (t+1)}$ 11:  $P(t+1)=\overline{P}\Delta (t+1)+[I-\Delta (t+1)]$ 12:  $x(t+1)=P(t+1)x\left(t\right)$ 13:until$x\left(t\right)$ converges