The fractions of the links of different types. The fractions of critical, ordinary and redundant links among the whole link set in the HLMN are shown in A). Few links are critical and most links are ordinary, which implies that there are only a few reactions whose failure could cause the increase of the minimum number of driver nodes. The fractions of the core high (CH), core moderate (CM) and non-core (NC) reaction links among the set of critical, ordinary, redundant links or the set of all the links (Ensemble) are shown in B). The fraction of the core high reaction links is the smallest and the fraction of non-core reaction links is the biggest in the set of critical links, which means that the reactions represented by critical links tend to be the non-core reactions in the human liver metabolic network.