Fig. 3

A graphical example that illustrates the CI-MDS model. A minimum dominating set (MDS) is defined as an optimized subset of proteins (red nodes) from which each remaining (i.e., NMDS) protein (white nodes) can be reached by at least one interaction. For the given toy network, there exists three different MDS configurations : (a) {3, 4}, (b) {3, 5} and (c) {3, 6}. Therefore, it is difficult to determine which one is the real set of controller nodes according to the standard MDS model. To overcome this problem, we introduce a CI-MDS model which takes into account the collective influence of proteins. Here we compute the collective influence of each protein with ℓ=1 (above the nodes). The collective influence of protein 4 is higher than those of proteins 5 and 6. According to the CI-MDS model, proteins {3, 4} are determined as an optimal MDS because its members have the highest collective influence among all the three possible MDS configurations