In recent years, the thriving development of research related to egocentric videos has provided a unique perspective for the study of conversational interactions, where both visual and audio signals play a crucial role. While most prior work focus on learning about behaviors that directly involve the camera wearer, we introduce the Ego-Exocentric Conversational Graph Prediction problem, marking the first attempt to infer exocentric conversational interactions from egocentric videos. We propose a unified multi-modal framework---Audio-Visual Conversational Attention (AV-CONV), for the joint prediction of conversation behaviors---speaking and listening---for both the camera wearer as well as all other social partners present in the egocentric video. Specifically, we adopt the self-attention mechanism to model the representations across-time, across-subjects, and across-modalities. To validate our method, we conduct experiments on a challenging egocentric video dataset that includes multi-speaker and multi-conversation scenarios. Our results demonstrate the superior performance of our method compared to a series of baselines. We also present detailed ablation studies to assess the contribution of each component in our model.