TITLE: Category of graphs.
QUESTION [5 upvotes]: Hello, I'm writting something about Malcev categories and monadicity. The fact is that I need to know if Graph is or not complete (have all finite limits). It seems easy but I would like a real answer (not my feelings saying that it is) and I don't find that information anywhere.
Thank you for your answers.

REPLY [3 votes]: Consider the category G that has exactly two distinct objects (call them a and b) and two distinct arrows a->b. A graph is precisely a functor G -> Set. This means that the category of graphs is a presheaf category. The rest follows.