I am having difficulties getting my captions centered underneath my graphs. I understand captions should be centered automatically. The funny thing is, if the caption is short enough it gets centered. However for example the following one does not:
Nevertheless, if I supplement your code snippet to a complete document, I can reproduce the problem. It seems to be better if you use the caption package and typeset the source of your figure as a second caption which is unnumbered.
However, the caption package supports line breaks in captions. If the complete caption is short enough (and the option singlelinecheck=on is active which is the default) they even are centered without any further setup as long as you use \\ and not\newline:
In your original code this does not work, because the caption is too long and the lines are left-aligned. However, caption has a solution for this, too: \captionsetup{justification=centering}. You can use this for all captions by placing it in the preamble or for one caption only by placing it in the {figure} environment where you want this: