How to use sudo and a graphical program?

[Kevin O'Gorman]

I guess I don't understand access permissions to my display.

If I become root via "sudo su -", I cannot use gedit or gvim because
they are unable to open the display.

If I start them as "sudo gedit somefile" it works, but when I'm doing
serious admin work, I consider this tedious.

I'm not complaining so much as wanting to understand.  Any clues?

-- 
Kevin O'Gorman, PhD