Fig. 4: Robustness analysis of synthetic networks, using adaptive centrality measures.

Disintegration of different network topologies, including Barabasi–Albert, Erdős–Rényi, random geometric, stochastic block model, and Watts–Strogatz models is considered. The robustness of an ensemble of each network model is tested against random failures and targeted attacks based measures of node centrality including betweenness, load, clustering, eigenvector, PageRank, closeness, current flow closeness, harmonic, subgraph, degree, and entanglement at three temporal scales (-small, -mid, -large), the last one introduced in this study and represented by dashes for more clarity (a). In contrast with Fig. 3, here, all these centrality measures are used in adaptive fashion—i.e., the ranking of the nodes according to every measure is updated after each node removal. Similar to the static analysis, the entanglement centrality, tuned at relatively large propagation time-scale, performs equal or faster than other measures in breaking the network up to its critical fraction (b). Except for entanglement at small and middle scales, the centrality measures presented in the boxes at the bottom are ordered according to the overall performance of the considered measures, across all numerical experiments.