The core brain regions responsible for basic human emotions are not yet fully understood. We investigated the key areas responsible for emotion recognition of facial expressions of happiness and sadness using data obtained from patients who underwent local brain resection. A total of 44 patients with right cerebral hemispheric brain tumors and 33 healthy volunteers were enrolled and subjected to a facial expression recognition test. Voxel-based lesion-symptom mapping was performed to investigate the relationship between the accuracy of emotion recognition and the resected regions. Consequently, trade-off relationships were discovered: the posterior-prefrontal region was related to a low score of happiness recognition and a high score of sadness recognition (disorder-of-happiness group), whereas the medial orbitofrontal region was related to a low score of sadness recognition and a high score of happiness recognition (disorder-of-sadness group). The emotion recognition score in both the happiness and sadness disorder groups was significantly lower than that in the control group (p = 0.0009 and p = 0.021, respectively). Interestingly, the deficit in happiness recognition was temporary, whereas the deficit in sadness recognition persisted during the chronic phase. Using graph theoretical analysis, we identified structural connectivity between the posterior-prefrontal and medial orbitofrontal regions. When either of these regions was damaged, the tract volume connecting them was significantly reduced (p = 0.013). These results indicate that the posterior-prefrontal and medial orbitofrontal regions may be crucial for maintaining a balance between happiness and sadness recognition in humans. Investigating the clinical impact of certain area resections using lesion studies combined with connectivity analysis is a useful neuroimaging method for understanding neural networks.