Controllability of complex networks: Choosing the best driver set

Power Grids as Complex Networks: Resilience and Reliability Analysis

“…In addition to the aforementioned centrality measures, which sometimes do not work well in CDNs [40], Spectral Centrality (SC) metrics have been introduced using eigendecomposition of the original or a modified version of the adjacency or Laplacian matrices of the network. It is shown that the spectrum of these matrices has a significant impact on collective behaviours in CDNs [38,[254][255][256]. For example, the variation of frequency in a distributed generation system is a function of the spectrum of its graph [109,257].…”

“…For example, the variation of frequency in a distributed generation system is a function of the spectrum of its graph [109,257]. Network spectrum is also important in the control of a CDN [101,254,258].…”

How Centrality of Driver Nodes Affects Controllability of Complex Networks

“…Thus, the properties that our work found can serve as references for other works to design networks. For example, for previous work [22], our results can be used as a reference to design a more efficient centrality measure. For previous work [23], our findings can serve as a partial guidance to design an optimal placement strategy.…”

“…There also have been many related works on how to choose driver nodes focusing on centrality measures. Moradiamani et al [22] proposed a new centrality measure and compared with the cases with the driver nodes with the proposed measure and the cases with other centrality measures. Jalili et al [23] also proposed an optimal placement strategy and discussed the difference between effects of the chosen nodes from the proposed method and the nodes with different network centrality on the controllability of networks.…”

“…Seven popular metrics of nodal centrality, including in-degree, out-degree, betweenness, closeness, eigenvector, Katz and PageRank, are studied to show the tendencies of driver nodes towards various nodal centralities. Many previous valuable works are dedicated to proposing new centrality measures [22], finding driver nodes or key nodes [9], designing an optimal placement strategy [23] or designing attacking strategies [26], but our paper focuses on studying the properties of driver nodes in terms of their centralities in detail. Our contributions are as follows: (1) The tendencies of driver nodes towards various nodal centralities are studied.…”