Before revision:  Here we present fast algorithms to calculate that variance in arbitrary graphs and forests. As for the latter, the algorithm calculates variance in linear time with respect to the number of vertices. This paves the way for many applications that rely on an exact but fast calculation of that variance. These algorithms are based on novel arithmetic expressions for the calculation of the variance that we develop from previous theoretical work  .
After revision:  Here we present fast algorithms to calculate that variance in arbitrary graphs in o(nm^2)-time, and in forests in O(n)-time. These algorithms work on a wide range of random layouts (not only on Moon's) and are based on novel arithmetic expressions for the calculation of the variance that we develop from previous theoretical work .