links matter. Furthermore, because of the chaotic dynamics and weak coupling, the influence of a single node on the rest of the network corresponds essentially to a random signal that is superposed to the randomness generated by the chaos in the local dynamics. The existing reconstruction techniques fail to reconstruct a model from the data, as they require the interaction to be of the same magnitude as the isolated dynamics.

In this paper, we introduce the notion of an [*effective network*]{}. Its aim is to make a model of a complex system from observations of the nodes evolution when the network has heterogeneous structure, the strength of interaction is small and local dynamics are highly erratic. This approach starts by reconstructing the local dynamics from observations of nodes with relatively few connections, and then recovers the interaction function from observations of the highly connected nodes whose dynamics are the most affected by the interactions as a result of the multitude of connections they receive from the rest of the networks[@park2013; @pereira2017]. A key achievement is that we are able to identify community structures even in the presence of weak coupling. An outcome of the effective network is that it recovers 