methods. The former identify the presence and strength of a connection between two nodes by measuring the [*dependence*]{} between their time-series in terms of: correlations [@de2004discovery; @reverter2008combining], mutual information [@butte1999mutual], maximum entropy distributions [@braunstein2008inference; @cocco2009neuronal], Granger causality, and causation entropy [@bressler2011wiener; @ladroue2009beyond]. Such methods alone do not provide information on the dynamics of the network, which is necessary to predict critical transitions. Model-based methods instead provide estimates (or assume a priori knowledge) of the dynamics and interactions in the system, and use this knowledge to reconstruct the network topology. When the interactions are sufficiently strong, the network structure can be recovered [@casadiego2017; @han2015; @wang2016]. For a more extensive account of reconstruction (model-free and -based) methods see the reviews [@wang2016; @nitzan2017revealing; @stankovski2017] and references therein.

In many real-world applications, the behaviour of isolated nodes is erratic (*chaotic*) and the interaction is weak [@schneidman2006; @haas2015; @kandel2000]. Moreover, the network structure typically has community structures and hierarchical organisations such as the rich-club networks found in the brain [@heuvel2011]. As the interaction strength per connection is weak and the statistical behaviour of the nodes robust, the influence of a single link on the overall dynamics is negligible and only the cumulative contribution of many 