I recently learned Graph Theory in the university, and i don't feel i have the intuitive approach to solve the problems i am facing there.
In the high school i remembered i was very talented in geometric branch, even the teacher recommended about me to go to competitions and be representative of my school.
The last days i was tought about it, Graph Theory should be closed connection to Geometric, because both required the ability to solve problems about pictures and patterns you see not like algebra that can be kind of tricky technique sometimes.
I wondered about it days, and i tried to analyse and search for explanation:
When i am facing Graph Theory problems and exercises, most of the times i am neglecting the illustration of the problem, and hence i try to imagine the graph and the solution on my head, what my take alot of processing power that can prevent me reach to the solution itself.
In the high school, the exercises in Geometric was drawn on the book so i have the illustration already.
I would be happy to hear your opinion on the subject.
Unfortunately the answer is "no". Being good in geometry does not necessarily imply being good in Graph theory, even if you have excellent visualisation skills. The thing is that Graph theory requires a thorough combinatorial skill, which is usually not acquired by solving high-school geometry problems.
I hope this helps.