The control of complex networks is affected by their structural characteristic. As a type of key nodes in a network structure, cut vertexes are essential for network connectivity because their removal will disconnect the network. Despite their fundamental importance, the influence of cut vertexes on network control is still uncertain. Here, we reveal the relationship between cut vertexes and driver nodes, and find that driver nodes tend to avoid cut vertexes. However, driving cut vertexes reduces the energy required for controlling complex networks, since the cut vertexes are located near the middle of the control chains. By employing three different node failure strategies, we investigate the impact of cut vertexes failure on the energy required. The results show that cut vertex failures markedly increases the control energy because cut vertexes are larger-degree nodes. Our results deepen the understanding of the structural characteristic in network control.
Numerous real-world systems can be naturally modeled as multilayer networks, enabling an efficient way to characterize those complex systems. Much evidence in the context of system biology indicated that the collections between different molecular networks can dramatically impact the global network functions. Here, we focus on the molecular multiplex networks coupled by the transcriptional regulatory network (TRN) and protein-protein interaction (PPI) network, exploring the controllability and energy requiring in these types of molecular multiplex networks. We find that the driver nodes tend to avoid essential or pathogen-related genes. Yet, imposing the external inputs to these essential or pathogen-related genes can remarkably reduce the energy cost, implying their crucial role in network control. Moreover, we find that lower minimal driver nodes as well as energy requiring are associated with disassortative coupling between TRN and PPI networks. Our findings in several species provide comprehensive understanding of genes' roles in biology and network control.
Despite the significant advances in identifying the driver nodes and energy requiring in network control, a framework that incorporates more complicated dynamics remains challenging. Here, we consider the conformity behavior into network control, showing that the control of undirected networked systems with conformity will become easier as long as the number of external inputs beyond a critical point. We find that this critical point is fundamentally determined by the network connectivity. In particular, we investigate the nodal structural characteristic in network control and propose optimal control strategy to reduce the energy requiring in controlling networked systems with conformity behavior. We examine those findings in various synthetic and real networks, confirming that they are prevailing in describing the control energy of networked systems. Our results advance the understanding of network control in practical applications.
Numerous real-world systems can be naturally modeled as multilayer networks, providing an efficient tool to characterize these complex systems. Although recent progress in understanding the controlling of synthetic multiplex networks, how to control real multilayer systems remains poorly understood. Here, we explore the controllability and energy requirement of molecular multiplex networks coupled by transcriptional regulatory network (TRN) and protein-protein interaction (PPI) network from the perspective of network structural characteristics. Our findings reveal that the driver nodes tend to avoid essential or pathogen-related genes. However, imposing external inputs on these essential or pathogen-related genes can remarkably reduce the energy cost, implying their crucial role in network control. Moreover, we find that the minimal driver nodes, as well as the energy required, are associated with disassortative coupling between TRN and PPI networks. Our results provide a comprehensive understanding of the roles of genes in biology and network control across several species.
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