I don't know about running, but I noticed by chance that one cemetery on my bike commute has a "no biking" sign on the gate. I had never thought about it (nor considered riding through there), but I can understand that any mourners or visitors would not appreciate yellow-clad bike commuters zipping through there at full blast.

If there are no signs about it, I'm guessing that moving through with respect and in accordance with the dignity of the place is fine.

I love walking through strange cemeteries, they're filled with so much history.