Emotional stimuli have evolutionary significance for the survival of organisms; therefore, they are attention-grabbing and are processed preferentially. The neural underpinnings of two principle emotional dimensions in affective space, valence (degree of pleasantness) and arousal (intensity of evoked emotion), have been shown to be dissociable in the olfactory, gustatory and memory systems. However, the separable roles of valence and arousal in scene perception are poorly understood. In this study, we asked how these two emotional dimensions modulate overt visual attention. Twenty-two healthy volunteers freely viewed images from the International Affective Picture System (IAPS) that were graded for affective levels of valence and arousal (high, medium, and low). Subjects' heads were immobilized and eye movements were recorded by camera to track overt shifts of visual attention. Algebraic graph-based approaches were introduced to model scan paths as weighted undirected path graphs, generating global topology metrics that characterize the algebraic connectivity of scan paths. Our data suggest that human subjects show different scanning patterns to stimuli with different affective ratings. Valence salient stimuli (with neutral arousal) elicited faster and larger shifts of attention, while arousal salient stimuli (with neutral valence) elicited local scanning, dense attention allocation and deep processing. Furthermore, our model revealed that the modulatory effect of valence was linearly related to the valence level, whereas the relation between the modulatory effect and the level of arousal was nonlinear. Hence, visual attention seems to be modulated by mechanisms that are separate for valence and arousal.