A method for finding the most vital edge based on the characteristic of network communication is proposed. The link importance is determined by its using frequency in all-pairs shortest paths and the most vital edge results in the highest frequency. Without the commonly used edge-deletion and edge-contraction methods, the proposed algorithm directly reflects the edge's contribution to the network communication and the relative importance of the two edges in the network can be evaluated. The algorithm analyses and the experimental results show that this algorithm overcomes the currently existent problems and provides a more reasonable principle for ranking edges which is consistent with our intuitive judgments.