On the minimum driver node set of \(k\)-uniform linear hypertree networks. (English) Zbl 07894928
Summary: The exact controllability research framework of complex networks points out that the controllability of the network has a great relationship with the minimum number of driver nodes. It is generally believed that the smaller the minimum number of driver nodes and the lower the cost of external control of the whole network to achieve the ideal state, the better the controllability of networks. In this paper, the minimum driver node problem of a hypernetwork is transformed into the maximum multiplicative problem of the eigenvalue of its 2-section graph. The minimum driver node numbers of two types of typical \(k\)-uniform hypertree networks are described, and their bounds are also given. By designing an algorithm, the method of characterizing the driver node set is obtained, and it is found that the selection of the minimum driver nodes of the network tends to the nodes with low hyperdegree. In addition, the paper verifies the minimum driver node set and the theoretical analysis results of controllability by simulation analysis.
MSC:
| 93B05 | Controllability |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 93B60 | Eigenvalue problems |
| 93C05 | Linear systems in control theory |
Keywords:
uniform hypernetwork; exact controllability; 2-section graph; minimum driver node set; algorithmReferences:
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