Then they introduce a new matrix $M$ which counts the number of times a link appeared before continuously (without a blink):

$$ M(\ell,r,y) = \sum_{n = 0}^{y-1} \prod_{m = y-n}^{y} \rho(\ell,r,m) $$

I.e. it counts the length of the maximal run of 1's, going backwards from year $y$.