Automatic modulation identification (AMI) is a technique to detect the modulation type and order of a received signal, which has the potential to enhance cognitive radio capabilities for future generations of communication devices. However, AMI classifiers traditionally have exhibited low efficiency in low signal-to-noise ratio (SNR) environments. Hence, to address this problem we present our novel Gated Graph Convolutional Neural Network (GGCNN) classifier for feature-based AMI. This architecture includes a robust feature extraction stage to extract deep correlative patterns about the received symbols. Not only does this feature extraction stage use the temporal characteristics of the received symbols, but it also takes advantage of embedded signaling features from the received signal. In the proposed classifier, the received constellations are treated as a graph, allowing it to outperform state-of-the-art classifiers due to its strong performance in graph classification. This is observed clearly in the visualization of the extracted features, even for high-order modulation schemes. In this paper, we present our systematic research conducted for maximizing the efficiency obtainable by our classifier. Extensive simulation results demonstrate a significant accuracy improvement of 18.44 percentage points, and an efficiency increase by 60.78% for our GGCNN-AMI classifier compared to state-of-the-art classifiers in low-SNR environments.