Q: my Macbook Pro suffers from spontaneous restarts, indicating something is wrong with graphics. Problem came with El Capitan I believe. Anybody familiar?

It is possible your upgrade went awry but it is also possible that you have a hardware problem. Your computer may have AHT built in - try restarting holding the D key - or you may need to use the installation DVD that came with the computer. If so put the DVD in the computer and hold the D key as you restart. Run the extended diagnostics test. If the test reports an error you’ll need to take the computer to an authorized repair center or Apple store. If it doesn’t report an error it might still be a hardware flaw that is so intermittent that it doesn’t get caught all the time. This is one of the reason I always keep a bootable backup on an external drive. If the problem is software, my bootable backup (which is always one OS version older than my computer has installed) is a good test bed.

Could be this hardware problem:

MacBook Pro (15-inch, Mid 2010) intermittent black screen or loss of video Quality Program has ended - Apple Support