early morning safety in the slope

Hi - I did a search on this and it turned up a thread from a year and a half ago. Sorry to repeat but I wanted some more current opinions.

Does anyone run early in the park, like between 6:30 a.m. and 7:30 a.m.? I just moved here and am wondering if the park is safe for a woman at that time. When I was running there this weekend, there were parts in the south and east part of the park that felt like they could be kind of isolated in the early morning.

Also, a related question - how are the streets in the north slope at that time? I don't leave for work until 9 or so and have yet to be out that early, but in my old Manhattan neighborhood, 6:30 a.m. was a completely isolated time and I actually had more than one scary confrontation just walking a few blocks to the gym in the morning. I'm curious about those mornings when I either have to go to work early or want to hit the gym instead of the park.

I apologize if this has been covered - like I said, I did do a search and have read past threads, but they are from a while ago. Any thoughts would be appreciated.