Fig. 7: Algorithmic complexity.

The algorithmic complexity of entropy computations is compared, between the (a) exact and (b) approximated entropy. Red dots indicate the average computation time over five realizations of Barabasi–Albert networks of different number of nodes, with attachment parameter m = 3. Note that the error bars, defined as standard deviation, corresponding to the exact entropy plot are negligible. The dashed lines show the regression with polynomials of orders 1, 2, and 3. Below, four panels show the high Spearman correlation between the ranking provided by exact and approximated versions of the entanglement for (c) Barabasi–Albert, (d) Erdos–Renyi, (e) Stochastic block model, and (f) Watts–Strogatz networks. Each plot shows one realization of one of the members of the synthetic network ensemble, used through this paper. In these plots, each dot corresponds to a node, where y and x axes indicate the approximated and exact entanglement of the node, respectively. The Spearman correlations of exact and approximate entanglement of nodes are reported on top of the plots.