Pairwise correlations are currently a popular way to estimate a large-scale network (> 1000 nodes) from functional magnetic resonance imaging data. However, this approach generally results in a poor representation of the true underlying network. The reason is that pairwise correlations cannot distinguish between direct and indirect connectivity. As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not. In a simulation study and an application to resting-state fMRI data, we compare the performance of pairwise correlations in large-scale networks (2000 nodes) against three other methods that are designed to filter out indirect connections. Recovery methods are evaluated in four simulated network topologies (small world or not, scale-free or not) in scenarios where the number of observations is very small compared to the number of nodes. Simulations clearly show that pairwise correlation networks are fragmented into separate unconnected components with excessive connectedness within components. This often leads to erroneous estimates of network metrics, like small-world structures or low betweenness centrality, and produces too many low-degree nodes. We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks. However, even with these methods, the presence of hubs in the generating network can be problematic if the number of observations is too small. Additionally, we show for resting-state fMRI that partial correlations are more robust than correlations to different parcellation sets and to different lengths of time-series.