At k-th step, Co-Simrank S k connects only two new hop-1 paths with the old retrieved paths S k−1 , whereas Co-Simmate R k connects two new hop-(2 k ) paths (by squaring the old hop-(2 k−1 ) paths) with the old retrieved paths R k−1 .
in each step of Co-Simrank, Co-Simmate is exponential steps faster than Co-Simrank.