Network Controllability

Minimum driver nodes (red) via maximum matching — Liu et al. 2011

Nodes: — | Driver nodes: — | n_D/N: — | Matching size: —

Nodes N: 20

Avg degree ⟨k⟩: 2.5

Network type

Kalman condition: system ẋ=Ax+Bu is controllable iff rank[B,AB,...,A^{n-1}B]=n.
Minimum driver nodes = N − |maximum matching| in the directed graph.
Scale-free networks: hubs reduce n_D; sparse random networks: n_D→N/2.