Network analysis is an emerging approach to functional connectivity in which the brain is construed as a graph and its connectivity and information processing estimated by mathematical characterizations of graphs. There has been little to no work examining the reproducibility of network metrics derived from different types of functional magnetic resonance imaging (fMRI) data (e.g., resting vs. task related, or pulse sequences other than standard blood oxygen level dependent [BOLD] data) or of measures of network structure at levels other than summary statistics. Here, we take up these questions, comparing the reproducibility of graphs derived from resting arterial spin-labeling perfusion fMRI with those derived from BOLD scans collected while the participant was performing a task. We also examine the reproducibility of the anatomical connectivity implied by the graph by investigating test-retest consistency of the graphs' edges. We compare two measures of graph-edge consistency both within versus between subjects and across data types. We find a dissociation in the reproducibility of network metrics, with metrics from resting data most reproducible at lower frequencies and metrics from task-related data most reproducible at higher frequencies; that same dissociation is not recapitulated, however, in network structure, for which the task-related data are most consistent at all frequencies. Implications for the practice of network analysis are discussed.