How much is too much when it comes to diagrams in a research article? This is actually specific to mathematics. In particular, in the sub field of category theory, differential geometry, algebraic geometry.
Question is as mentioned above.

How much is too much when it comes to diagrams in a research article?
Do more diagrams annoy a reader?

I did not expect this question to create so much confusion. May be some one who has experience (don’t ask how much) in reading research articles in mathematics (pure mathematics, if that makes some difference) can say something relevant as it differs from one field to another field.
By diagram, I do not mean graphs. I want to explain the setup in diagrams. I do not know if it reach correctly but,  I want to add diagram of heart and not graph of case study how many times it beats in different persons of different age or something like that.
That entirely depends on the article itself. In some cases diagrams aid an explanation and make it clearer. In others they offer little insight. If an article depends on having many diagrams of the former kind, then I don't see that "too many" is an issue. But even a few of the latter kind may just get in the way of understanding. 

Words and pictures can be complementary. It is a judgement call by the authors as to which is best in a given case. They may err a bit, but that is human nature. 

In general, think about whether words or pictures/figures better convey your meaning and act accordingly. Sometimes both are needed. Examples illustrating (note the word) a concept are often best presented in figures. Imagine a Calculus textbook without figures. Now imagine one without formulae. Would either work?