Here are a few examples of deep intensive and perhaps obsessive love:
1. They are (sexually) possesive
2. They have an intense longing and craving to be with you emotionally, not just physically/sexually
3. Obsession -- they think about you a lot -- day and night
4. They would die for you
5. You are the center of their world
6. They find no (or very little) fault in you
7. They feel a rush from you
8. When they are or feel rejected -- they are deeply sad and experience a great deal of pain
9. They believe you are different from every woman that exists.
10. They become very moody -- when things don't appear to work out with you they have a great sadness, and they are very happy/high when things are going well with you.
from Love Anthropologist Helen Fisher