Co-authored publications across sectors have been used as indicators of the triple helix model and more generally for the study of science–technology relations. However, how to measure the relationships among the three or more sectors is a technically difficult issue. Using mutual information as an indicator has proved to be effective, but it is not widely used. In this paper, we introduced φ coefficients and partial correlation as conventional indicators to measure the relationships among sectors on the basis of Japanese publication data in the ISI-databases. We also proposed a new approach of graphical modeling based on partial correlation for studying university–industry–government relationships and relationships with other sectors. The conventional indicators give results that are consistent with mutual information, which shows that collaborations among the three national sectors (U, I, G) are getting weaker and that members of these sectors tend to collaborate much more with foreign researchers. It is also shown that universities used to play the central role in the national publication system and acted as a bridge between national sectors and foreign researchers. However, since 2000, the situation has been changing. The center of the Japanese research network is becoming more “foreign” oriented.