Although recent writings indicate the importance of personal contact structures in diffusing innovations and in determining perceptions, the internal contact structure of the school faculty remains unexamined. This study applies directed graph theory, a new branch of mathematics, to analyzing school contact structure. Sociometric data and perceptions of the school were collected from 48 elementary school faculties containing 1,121 people. Using directed graph theory, 12 indices of the contact structure were derived from the sociometric data and entered into canonical correlations and factor analyses with perceptions of the school, such as faculty innovativeness. Several significant relationships were obtained. (Author)