The brain consists of a number of sub-networks dedicated to several perceptual/cognitive functions, and allocates neural resources depending on cognitive demands. Recent studies on resting-state functional connectivity have shown competitive patterns of the functional sub-networks: 'task-negative' default mode networks and 'task-positive' networks. In this study, we employed the functional connectome approach to study the brain functional networks derived from fMRI data. Several graph theoretical measurements were employed to quantitatively investigate differences in global and local information transfer efficiency calculated between rest and task experimental conditions. Our results have suggested that normalized clustering coefficient was larger during rest compared to task, indicating more local efficiency of information transfer during rest, while small-worldness was preserved. In addition, the betweenness centrality of nodes was larger for task than rest at the orbital part of right superior frontal gyrus, the orbital part of right middle frontal gyrus and right olfactory cortex. In contrast, this parameter was larger for rest at left fusiform gyrus. As a consequence of this analysis, we show that graph theoretical measurements can be powerful biomarkers for quantifying cognitive states considering efficiency of information transfer, which can differ based on cognitive needs.