Finding and analysing the minimum set of driver nodes required to control multilayer networks

It is difficult to control multilayer networks in situations with real-world complexity. Here, we first define the multilayer control problem in terms of the minimum dominating set (MDS) controllability framework and mathematically demonstrate that simple formulas can be used to estimate the size of the minimum dominating set in multilayer (MDSM) complex networks. Second, we develop a new algorithm that efficiently identifies the MDSM in up to 6 layers, with several thousand nodes in each layer network. Interestingly, the findings reveal that the MDSM size for similar networks does not significantly differ from that required to control a single network. This result opens future directions for controlling, for example, multiple species by identifying a common set of enzymes or proteins for drug targeting. We apply our methods to 70 genome-wide metabolic networks across major plant lineages, unveiling some relationships between controllability in multilayer networks and metabolic functions at the genome scale.