A new methodology based on complex network analysis is applied to the CMIP5 climate model simulations to assess their performances, quantify uncertainties, and uncover changes in global linkages between past and future projections. Network properties of modeled sea surface temperature (SST) and precipitation over 1956-2005 are constrained towards observations or reanalyses, and their differences quantified using two metrics. Projected changes from 2051 to 2300 under the scenario with the highest Representative and Extended Concentration Pathways (RCP8.5 and ECP8.5) are then determined. The network of models capable of reproducing well major climate modes in the recent past, change little during this century. In contrast, among those models the uncertainties in the projections after 2100 are substantial, and are primarily associated with divergences in the representation of the modes of variability, particularly of the El Nino Southern Oscillation (ENSO), and their connectivity, and therefore with their intrinsic predictability, more so than with differences in the mean state evolution.