Figure 4: Values of η for real data sets.
From: Energy scaling of targeted optimal control of complex networks
(a) We compute the maximum control energy required for the s420st circuit network and the TM metabolic network for increasing target node fraction, p/n. Each point represents the mean of 50 realizations where each realization is a specific choice of the nodes in the target node set. Error bars represent one s.d. (b) The same analysis performed for the Carpinteria food web, the protein structure 1 network and a Facebook forum network. Each point represents the mean of 50 realizations where each realization is a specific choice of the nodes in the target node set. Error bars represent one s.d. For both a and b, the linear behaviour exists only when the target fraction increases beyond p/n=0.1. (c) We numerically compute values of η for real data sets (compiled in Supplementary Table 1) for comparison when nd=0.45 or larger. The values of η are plotted against each network’s average degree as the degree distribution that best describes the degree sequence may or may not be scale-free. Nonetheless, we see a similar trend that low average-degree networks have a larger value of η, as demonstrated in Fig. 2c. Also worth noting is that networks from the same class (as defined in the legend) tend to have similar values of η.
