Eur. Phys. J. B (2015) 88: 168
https://doi.org/10.1140/epjb/e2015-60230-3

Regular Article

Analytical controllability of deterministic scale-free networks and Cayley trees

¹ Center for Nonlinear Complex Systems, Department of Physics, School of Physics Science and Technology, Yunnan University, Kunming, Yunnan 650091, P.R. China
² School of Mathematical Sciences, Kaili University, Kaili, Guizhou 556011, P.R. China
³ School of Computer Science and Technology, Baoji University of Arts and Sciences, Baoji, Shaanxi 721016, P.R. China

^a e-mail: kfcao163@163.com

Received: 3 November 2014
Received in final form: 23 March 2015
Published online: 1 July 2015

Abstract

According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their self-similarity, the analytical results of the exact controllability are obtained, and the minimum sets of driver nodes (drivers) are also identified by elementary transformations on adjacency matrices. For these two types of undirected networks, no matter their links are unweighted or (nonzero) weighted, the controllability of networks and the configuration of drivers remain the same, showing a robustness to the link weights. These results have implications for the control of real networked systems with self-similarity.