This study systematically analyzes the structural characteristics and enhancement strategies of college English teachers’ intercultural teaching competence through the integration of graph theory. A dynamic teaching competence model with three dimensions of curriculum design, facilitation and reflection was constructed, and structural equation modeling was used to verify the model fitness. The results of factor analysis showed that the total interpretation rate of the scale reached 84.714%, the result of X²/df showed 3.803<5, the value of RMR was 0.0280.90. The total effect of Curriculum Design Competence on Facilitation Skill is 0.391, and the total effect of Teaching Reflection Competence on Curriculum Design Competence and Facilitation Skill is 0.322 and 0.357 respectively, which identifies the indirect effect path of intercultural teaching ability of “Teaching Reflection Competence → Curriculum Design Competence → Facilitation Skill”. The indirect effect path of intercultural teaching ability is recognized. Based on the above conclusions, English teachers in colleges and universities should activate the leverage effect of reflective ability to drive the optimization of the ability structure.
