  Real-world complex systems such as ecological communities and neuron networks
are essential parts of our everyday lives. These systems are composed of units
which interact through intricate networks. The ability to predict sudden
changes in network behaviour, known as critical transitions, from data is
important to avert disastrous consequences of major disruptions. Predicting
such changes is a major challenge as it requires forecasting the behaviour for
parameter ranges for which no data on the system is available. In this paper,
we address this issue for networks with weak individual interactions and
chaotic local dynamics. We do this by building a model network, termed an
effective network, consisting of the underlying local dynamics at each node and
a statistical description of their interactions. We illustrate this approach by
reconstructing the dynamics and structure of realistic neuronal interaction
networks of the cat cerebral cortex. We reconstruct the community structure by
analysing the stochastic fluctuations generated by the network and predict
critical transitions for coupling parameters outside the observed range.
