Abstract: This paper uses the method of regular-triangle mapping to empirically analyze the collaboration between scientists. Based on the data of scientific collaboration networks, each scientist is mapped to a standard regular triangle based on the collaboration relationship with three nearest higher-influence scientists who satisfy a type of given condition. The modes of their relationship can be shown by the pattern of their mapping position in the regular triangle. We find that the distribution of scientists on the mapping triangle shows obvious center-gathering tendency, indicating the strong equilibrium property that the collaboration of scientists is often evenly distributed among multiple collaboration partners with higher-influence. This property can be observed in the full parameter space of all of the four research topics discussed in this paper, and the academic age, the difference in total citations and some other factors do not efficiently impact the expression of the equilibrium property. Furthermore, we find that the impact of the equilibrium property on the scientific influence of scientists mainly is negative. This research provides a new perspective for analyzing the pattern of collaboration relationships between scientists and the node relationships of various complex networks.