Despite many studies reporting hemispheric asymmetry in the representation and processing of emotions, the essence of the asymmetry remains controversial. Brain network analysis based on electroencephalography (EEG) is a useful biological method to study brain function. Here, EEG data were recorded while participants watched different emotional videos. According to the videos’ emotional categories, the data were divided into four categories: high arousal high valence (HAHV), low arousal high valence (LAHV), low arousal low valence (LALV) and high arousal low valence (HALV). The phase lag index as a connectivity index was calculated in theta (4–7 Hz), alpha (8–13 Hz), beta (14–30 Hz) and gamma (31–45 Hz) bands. Hemispheric networks were constructed for each trial, and graph theory was applied to quantify the hemispheric networks’ topological properties. Statistical analyses showed significant topological differences in the gamma band. The left hemispheric network showed significantly higher clustering coefficient (Cp), global efficiency (Eg) and local efficiency (Eloc) and lower characteristic path length (Lp) under HAHV emotion. The right hemispheric network showed significantly higher Cp and Eloc and lower Lp under HALV emotion. The results showed that the left hemisphere was dominant for HAHV emotion, while the right hemisphere was dominant for HALV emotion. The research revealed the relationship between emotion and hemispheric asymmetry from the perspective of brain networks.