Fig. 2: Comparison between the coupled and uncoupled cases.

Average precision–recall (PR) curves of the coupled (red) and uncoupled (blue) influence scores in the prioritization of essential (a) and cancer (b) genes. The gray PR curves represent 100 random node rankings. On the right of each plot are listed the average precision scores (APS) of the three ranking strategies evaluated from the corresponding PR curves. The performance of coupled influence scores in prioritizing essential and cancer genes are, respectively, 5.05% and 48.94% higher than that of uncoupled influence scores. In the coupled case, the removal of a single-gene not only causes one-time failures as those in the uncoupled cases but also causes a second or third round of cascading failures. The average numbers of nodes failing in the second round caused by the removal of essential (c) and cancer genes (d) are, respectively, higher than that of removing the nonessential and non-cancer genes, explaining why the coupled case performs better in prioritizing essential and cancer genes. In addition, the densities of e essential and f cancer genes among the top n genes ranked by influence scores (red diamonds) are higher than that ranked by out-degrees (black circles). For the genes of the same influence scores or of the same out-degrees, we randomly put their orders 100 times and compute the average densities. It indicates that the influence scores perform better than out-degrees in uncovering the connections between network topology and biological mechanisms.