This paper reports on an analysis of inter-human interaction in the presence of a humanoid robot, which provides us with important non-verbal information for establishing relationship among humans and robots, as well as a model for communication robots to estimate friendships among humans around them. Human-robot interactions recorded in videos are rich in useful information to develop the social abilities of communication robots, though there are many difficulties associated with analyzing them since these videos are qualitative data. We applied the observation method, which is a common psychological method for analyzing qualitative data, to analyze the interaction among children and a robot in an elementary school. We established a model to estimate friendships among children from their non-verbal interaction with each other using factors such as by touch, gaze, and distance between them. The results revealed a gender difference in their non-verbal interactions, and by separating the model into different components for each gender, we were able to discriminate between friendly and non-friendly relationships among the children, with a 74.5% accuracy for males and an 83.8% one for females.