Trajectory prediction module in an autonomous driving system is crucial for the decision-making and safety of the autonomous agent car and its surroundings. This work presents a novel scheme called AiGem (Agent-Interaction Graph Embedding) to predict traffic vehicle trajectories around the autonomous car. AiGem tackles this problem in four steps. First, AiGem formulates the historical traffic interaction with the autonomous agent as a graph in two steps: (1) at each time step of the history frames, agent-interactions are captured using spatial edges between the agents (nodes of the graph), and then, (2) connects the spatial graphs in chronological order using temporal edges. Then, AiGem applies a depthwise graph encoder network on the spatial-temporal graph to generate graph embedding, i.e., embedding of all the nodes in the graph. Next, a sequential Gated Recurrent Unit decoder network uses the embedding of the current timestamp to get the decoded states. Finally, an output network comprising a Multilayer Perceptron is used to predict the trajectories utilizing the decoded states as its inputs. Results show that AiGem outperforms the state-of-the-art deep learning algorithms for longer prediction horizons.