Emotion recognition in conversation (ERC) has received much attention, lately, from researchers due to its potential widespread applications in diverse areas, such as health-care, education, and human resources. In this paper, we present Dialogue Graph Convolutional Network (DialogueGCN), a graph neural network based approach to ERC. We leverage self and inter-speaker dependency of the interlocutors to model conversational context for emotion recognition. Through the graph network, DialogueGCN addresses context propagation issues present in the current RNN-based methods. We empirically show that this method alleviates such issues, while outperforming the current state of the art on a number of benchmark emotion classification datasets.