Internet chat programs and instant messaging services are becoming increasingly popular among Internet users. One of the crucial issues with Internet chat is how to manage the corresponding pairs of questions and answers in a sequence of conversations. Although many novel methodologies have been introduced to cope with this problem, most are poor in managing interruptions, organizing turn-taking, and conveying comprehension. The Internet environment is recently evolving into a 3D environment, but the problems with managing chat dialogues with the standard 2D text-based chat have remained. Therefore, we propose a more realistic communication model for chat agents in 3D virtual space in this paper. First, we propose a new method to measure the capacity of communication between chat agents and a novel visualization method to depict the hierarchical structure of chat dialogues. In addition, we are concerned with communication networks for virtual people (avatars) living in virtual worlds. In this paper we consider a microscopic aspect of a social network in a relatively short period of time. Our experiments show that our model is highly effective in a virtual chat environment, and the communication network based on our model greatly facilitates investigation of a very large and complicated communication network.