The fact that the climate on the earth is a highly complex dynamical system is well-known. In the last few decades great deal of effort has been focused on understanding how climate phenomena in one geographical region affects the climate of other regions. Complex networks are a powerful framework for identifying climate interdependencies. To further exploit the knowledge of the links uncovered via the network analysis (for, e.g., improvements in prediction), a good understanding of the physical mechanisms underlying these links is required. Here we focus on understanding the role of atmospheric variability, and construct climate networks representing internal and forced variability using the output of an ensemble of AGCM runs. A main strength of our work is that we construct the networks using MIOP (mutual information computed from ordinal patterns), which allows the separation of intraseasonal, intraannual and interannual timescales. This gives further insight to the analysis of climatological data. The connectivity of these networks allows us to assess the influence of two main indices, NINO3.4 – one of the indices used to describe ENSO (El Niño–Southern oscillation) – and of the North Atlantic Oscillation (NAO), by calculating the networks from time series where these indices were linearly removed. A main result of our analysis is that the connectivity of the forced variability network is heavily affected by “El Niño”: removing the NINO3.4 index yields a general loss of connectivity; even teleconnections between regions far away from the equatorial Pacific Ocean are lost, suggesting that these regions are not directly linked, but rather, are indirectly interconnected via El Niño, particularly at interannual timescales. On the contrary, on the internal variability network – independent of sea surface temperature (SST) forcing – the links connecting the Labrador Sea with the rest of the world are found to be significantly affected by NAO, with a maximum at intraannual timescales. While the strongest non-local links found are those forced by the ocean, the presence of teleconnections due to internal atmospheric variability is also shown.