In recent years, with the continuous growth in the number of international graduate students coming to China, international graduate education has become an important part of graduate education, which bears on the effectiveness of universities’ “double first-class” initiative. This paper probes into the characteristics and influencing factors of the interactive relationship among 354 science and engineering international graduate students in “double first-class” universities through a questionnaire based on the interpersonal circle model. It is found that the interactive relationship presents the core characteristics of leadership, and gender, continent, grade and cross-cultural adaptability have significant differences on the relationship. Graduate students have a good satisfaction with the relationship. The relationship characteristics of leadership, helpfulness/friendliness and understanding have a significant positive impact on satisfaction, while the relationship characteristics of dissatisfaction and hesitation have a significant negative impact on satisfaction. The core characteristics of the ideal mentoring relationship are support and respect. It is suggested to strengthen the concept of teacher education and implement the role of whole process education, comprehensively improve the quality and cross-cultural adaptability of international graduates, establish supervision and assessment mechanisms and interactive exchange and sharing platforms to create a harmonious interactive atmosphere.