Abstract
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.
Highlights
In recent years, structural controllability and control theory approaches have been studied in depth in the context of linear and nonlinear complex systems and networks[1,2,3,4]
We investigate the controllability of multilayer networks using a minimum dominating set (MDS)[14] approach and focus on a generic type of multilayer network constructed in a manner similar to that of multiplex networks
The results show that this multilayer network problem can be quickly solved using the proposed method, in spite of the fact that the MDS is an NP-hard problem (see Fig. 3)
Summary
Structural controllability and control theory approaches have been studied in depth in the context of linear and nonlinear complex systems and networks[1,2,3,4]. Pósfai et al studied the controllability of multilayer linear discrete systems with time delays, where control signals are applied to only one layer[12] They showed that the minimum number of driver nodes for such systems can be computed based on the maximum network flow. These approaches are useful for controlling multilayer networks in which different layers are connected by some dynamics. Menichetti et al studied such type of multilayer network control[13] by extending the framework of the linear structural controllability of single-layer networks using the maximum matching approach[5]. We demonstrate that the size of the MDSM does not increase by much compared with that of the MDS for a single network if the difference among the layers in multilayer networks is small
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