Degree Correlation

r(G)=i=1nj=i+1n((didˉ)(djdˉ))A[i,j]i=1n(didˉ)2r(\boldsymbol{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}}