Recent resting-state functional magnetic resonance imaging (fMRI) studies using graph theory metrics have revealed that the functional network of the human brain possesses small-world characteristics and comprises several functional hub regions. However, it is unclear how the affective functional network is organized in the brain during the processing of affective information. In this study, the fMRI data were collected from 25 healthy college students as they viewed a total of 81 positive, neutral, and negative pictures. The results indicated that affective functional networks exhibit weaker small-worldness properties with higher local efficiency, implying that local connections increase during viewing affective pictures. Moreover, positive and negative emotional processing exhibit dissociable functional hubs, emerging mainly in task-positive regions. These functional hubs, which are the centers of information processing, have nodal betweenness centrality values that are at least 1.5 times larger than the average betweenness centrality of the network. Positive affect scores correlated with the betweenness values of the right orbital frontal cortex (OFC) and the right putamen in the positive emotional network; negative affect scores correlated with the betweenness values of the left OFC and the left amygdala in the negative emotional network. The local efficiencies in the left superior and inferior parietal lobe correlated with subsequent arousal ratings of positive and negative pictures, respectively. These observations provide important evidence for the organizational principles of the human brain functional connectome during the processing of affective information.