Figure 2: The variation of η with respect to model network parameters.
From: Energy scaling of targeted optimal control of complex networks
(a) The maximum control energy is computed for model networks constructed with the static model and the Erdos–Renyi (ER) model while varying the target node fraction. For the static model, four different power-law exponents are used. The average degree of each model network is kav=2.5 and its size is n=500. The input node fraction nd=0.5, chosen such that the pair (A, B) is controllable. Further aspects like edge weights and values along the diagonal of the adjacency matrix are discussed in the Methods section. Each set of target nodes is chosen randomly from the nodes in the network. Each point represents the mean value of the control energy taken over 50 realizations. The error bars represent one s.d. Note the linear growth of the logarithm of the control energy. The slopes of these curves are the values of η corresponding to each set of parameters. A linear fit curve is provided in grey. Also, as γ grows, that is, the scale-free models become more homogeneous, the slope approaches that of the Erdos–Renyi model. (b) The same study as in a except that kav=8.0. The same behaviour is seen but note the difference in scales of the vertical axis. Each point is the mean over 50 realizations, and error bars represent one s.d. (c) The study in a and b is performed for more values of kav, and the value of η is computed for each curve.
