Effect of correlations on controllability transition in network control
  The numerical controllability transition makes the success of control can be achieved by increasing the number of driver nodes to a certain point. Motivated by the fact that the degree correlation has vast role in the dynamics on networks, we study the impact of various degree correlations of different networks on the controllability transition point and find that the transition point depicts local maximum in sparse networks as degree correlation r around 0.1 and 0 in ER and SF networks respectively. With the increasing of average degree, the local maximum disappear and the controllability transition cannot be influenced by degree correlation and degree distribution in dense ER networks. The results are supported by numerical simulations and provide more details to estimate the minimal driver nodes in large networks. 
Sen Nie, Xuwen Wang, Binghong Wang
physics.soc-ph cond-mat.stat-mech math.OC