One hallmark example of a link between global topological network properties of complex functional brain connectivity and cognitive performance is the finding that general intelligence may depend on the efficiency of the brain's intrinsic functional network architecture. However, although this association has been featured prominently over the course of the last decade, the empirical basis for this broad association of general intelligence and global functional network efficiency is quite limited. In the current study, we set out to replicate the previously reported association between general intelligence and global functional network efficiency using the large sample size and high quality data of the Human Connectome Project, and extended the original study by testing for separate association of crystallized and fluid intelligence with global efficiency, characteristic path length, and global clustering coefficient. We were unable to provide evidence for the proposed association between general intelligence and functional brain network efficiency, as was demonstrated by van den Heuvel et al. (2009), or for any other association with the global network measures employed. More specifically, across multiple network definition schemes, ranging from voxel-level networks to networks of only 100 nodes, no robust associations and only very weak non-significant effects with a maximal R2 of 0.01 could be observed. Notably, the strongest (non-significant) effects were observed in voxel-level networks. We discuss the possibility that the low power of previous studies and publication bias may have led to false positive results fostering the widely accepted notion of general intelligence being associated to functional global network efficiency.