Hi - What you descirbe may not be hunger at all, but dehydration. Often dehydration symptoms manifest themselves as hunger. I would suggest you make small tweaks to your caloric intake, as suggested maybe a few more carbs and some protein, but you might want to really consider increasing your fluid intake before you run, during your run and after you run. Be mindful of your fluid intake throughout the day/night as well.
What would be helpful is to better understand your run - how far are you running? How long have you been running and what is your average pace/mile? The terrain your running and intensity? The recommendation on hydration is given off the cuff, since you don't provide the aformentioned details. If you are running 13 miles on rock trails, then I would augment my answer, but if you are running 5 miles in an hour I would give different advice.