Ohhhh, that's a major no no with running. After an overnight fast, you have near depleted (or depleted) liver glycogen. Thus, if you run without eating breakfast, your body must rely on other fuel sources (~body fat and body protein such as muscle/bone), which are less efficient energy sources and longterm could be a cause for injury/illness.
Girl, you need to get food in you before you run. Even if it's something small like a banana or fruit bar, you need to get your blood sugar up after an overnight fast. Just water won't cut it.