Degree Correlation

$r(\mathbf{G})=\frac{{\sum }_{i=1}^n{\sum }_{j=i+1}^n\left(\left(d_i-\bar{d}\right)\left(d_j-\bar{d}\right)\right)A[i,j]}{{\sum }_{i=1}^n{\left(d_i-\bar{d}\right)}^2}$