Figure 2

Target edge control based on switchboard dynamics and the k-travel theory. (a) The graph is the original network, and the target edges which are indicated in red. (b) The switchboard matrix of the original matrix. (c) The linear graph of the original network. The nodes in graph(c) are the edges in graph(a). (d) The driver nodes and the driven edges that we obtained by using SBD theory. According to the SBD, we need two driver nodes(indicated in green) and three driven edges(indicated in green) to control the whole network. If we want to control the target edges, we need two nodes(a and b) and three driven edges \((x\mathrm{1,}\,x\mathrm{2,}\,x\mathrm{5)}\). (e) In fact, we need only one node(a) and one driven edge(\(x1\)) to control the states of the target edges, which can be obtained according to the k-travel theory.