Doing graph theory after a thesis in pure mathematics I've just went through the 1st year of my PhD in France, it is related to Floer Homology. I didn't know what it was really about at that time, I chose this subject because I thought it would combine all the stuff I love (different facets of differential geometry, algebraic topology, functional analysis...) but I kind of regret this choice now : I may like to learn and discover such complex and in the same time beautiful theories, I don't feel like building them, to sum up, I'm a bit fed up with all the abstract nonsense ...
On the other way, I had to teach a basic course in graph theory, a topic I never had met before. I really fell in love with it, since then, I spent my time reading stuff about graph theory and now I would like to change my plans, I didn't get any useful answers on french forums so I'll try here :
-Is there a way, in France or abroad, to switch from my ongoing thesis to a PhD in graph theory? If not, is there a  (not too long) bridge between these two?
I know a lot of you are going to think that I'm just avoiding difficulty and that I'll fall into it again when reaching a higher level in graph theory but I've already went through with that question and I'd appreciate only answers really related to my question.
Thank you all for the attention!
 A: In the United States one usually spends 4-6 years in graduate school, and switching subjects and thesis advisors is quite common. In fact it is customary to start working on the actual thesis after the first or second year in graduate school. In Europe, switching is harder because the time in graduate school is usually limited to 3 years, and departments also tend to be smaller. What is worse, one has to choose a topic and sometimes even a thesis title before actually starting the graduate studies.
I don't think that graph theory is any closer to Floer homology than any other subject in mathematics. On the other hand, 2 years might be enough for you to write a thesis in graph theory, especially if you find an advisor who can guide you well. Another option that I recommend you to consider seriously: apply to graduate school again and start all over from scratch. It is definitely better "losing 1-2 years" at this point of your career than becoming a frustrated and miserable mathematician for a longer period (perhaps for life). Whatever you work on as a graduate student will have a huge effect on your later professional life.
Finally, a personal remark: I did switch subject and school during my graduate studies, and I have not regretted it (although many have advised me against it at that time).
