Strong structural control centrality of a complex network

We introduce the definition of strong structural control centrality, which represents the dimension of strong structurally controllable subspace or the capability of a single node to control an entire directed and weighted network in a strongly structural manner. A purely algebraic algorithm to calculate strong structural control centrality is proposed. Then we explore the quality of the strong structural control centrality. The relation between strong structural control centrality and the layer index in a directed tree inspires us to research (1) some fast methods to achieve strong structural control centrality and (2) the size relationship of strong structural control centralities of nodes belonging to different supernodes.