The continuous detection of emotional states has many applications in mental health, marketing, humancomputer interaction, and assistive robotics. Electrodermal activity (EDA), a signal modulated by sympathetic nervous system activity, provides continuous insight into emotional states. However, EDA possesses intricate nonstationary and nonlinear characteristics, making the extraction of emotionrelevant information challenging. We propose a novel graph signal processing (GSP) approach to model EDA signals as graphical networks, termed EDA-graph. The GSP leverages graph theory concepts to capture complex relationships in timeseries data. To test the usefulness of EDA-graphs to detect emotions, we processed EDA recordings from the CASE emotion dataset using GSP by quantizing and linking values based on the Euclidean distance between the nearest neighbors. From these EDA-graphs, we computed the features of graph analysis, including total load centrality (TLC), total harmonic centrality (THC), number of cliques (NoC), diameter, and graph radius, and compared those features with features obtained using traditional EDA processing techniques. EDA-graph features encompassing TLC, THC, NoC, diameter, and radius demonstrated significant differences (p<0.05) between five emotional states (Neutral, Amused, Bored, Relaxed, and Scared). Using machine learning models for classifying emotional states evaluated using leave-one-subject-out crossvalidation, we achieved a five-class F1 score of up to 0.68.