Electroencephalogram (EEG) monitors the brain’s electrical activity and carries useful information regarding the subject’s emotional states. Due to the nonstationary and being complex in nature, proper signal-processing techniques are necessary to get meaningful interpretations. The EEG signal has been represented using a graph by incorporating the temporal dependency. In this article, a novel feature based on spectral graph wavelet transform (SGWT) for representing EEG signals has been proposed by considering the interdependency among different samples of EEG signals. SGWT is effective in finding multiscale information at the local level as well as the global level. These multiscale representations allow for the extraction of information about the EEG signal at different scales. The SGWT coefficients are used to develop machine-learning classifiers for emotion identification. Principal component analysis (PCA) is also used for feature reduction. The proposed framework is evaluated based on a publicly available SEED dataset with the help of extensive experiments. The -nearest neighbor (KNN) classifier provides 97.3% accuracy with a standard deviation of 1.2%. The SGWT-based representation has achieved 12.7% higher accuracy compared to the raw EEG signal, which shows the usefulness of the proposed approach. Our model for emotion recognition attains superior classification performance compared to state-of-the-art methods. Finally, the investigation of interdependency among the samples of EEG signals reveals that the SGWT-based representation of EEG signals is a useful tool for analyzing EEG signals.