Where are the graphs?
There is a mod called Info Addict that shows graphs:
There are no graphs in the current version* of the game.
A quick search of the Manual for "graph" found only the demographics screen you mentioned. In playing I have also found no graphs.
You can get some useful info from the occasional popups telling who has the largest army, the most techs, the most gold, regardless who you have met.
*the current version being the game as first released. I'd mention the particular patch if I could find that info.
The current version of Civ 5 has graphs at the end of the game.