Fig 3. Consistency of NI within and between models and computational gain.

The consistency of ordering nodes according to their NI value, quantified by Kendall correlation rank τ within (a) the WM, (b) the CM, and (c),(d) comparison between the two models. The comparison is performed for networks of size N = 15, 30 and 50. In each scenario 10 realizations of directed random networks with mean degree c = 1.6, 3.2, and 5.3 are considered. For each case, the NI ranking is contrasted across 5 different parameter realizations. In panel (c) all combinations of parameters are compared, whereas in panel (d) the parameter set that maximizes τ is used. Although the distribution of NI tends to differ between the models as N increases, panel (d) shows that it is possible to find parameters such that the NI ordering is consistent between models. The red bars in panels (c) and (d) correspond to undirected scale-free networks (10 network realizations, N = 50, γ = 2, and c = 6). Panel (e) demonstrates the computational gain of using the CM relative to the WM. The gain corresponds to the computational time the WM takes to compute the BNI divided by the time the CM takes to perform the same task.