Fig. 7: Why do we need an early-warning signal?
From: Machine learning dismantling and early-warning signals of disintegration in complex systems
Toy-example meant to explain why the LCC is not sufficient to evaluate the state of the system: in (a) we show a toy-example network composed of two cliques connected by 10 bridges. The size of the nodes represents their betweenness value and the color (from dark red to white) represents their importance to the system’s health according to our method. As illustrated in (b) and (c), the LCC decreases at the same rate during the initial part of both a betweenness and an inverse betweenness-based attacks. Instead, Ω values do not and reach warning levels before the system suddenly collapses. Note that LCC and SLCC are the largest and second-largest connected components respectively, Ω is the early-warning descriptor introduced in this study, and PI is the pn value of each removed node.
