This is your problem and you say you have been studying "relations" so this graphic representation of relations should have been defined in your textbook. Also, there are several different notations used for relations, such as "R(x,y)= true" "x R y" and you did not say what notation you are used nor what definition of "relation" you are using.
The simplest definition of "relation of X with Y" I know is "a set of ordered pairs with the first member from set X and the second in Y".
Then we can represent each member of the relation as the ordered pair (x, y). The graphic representation has an arrow from x to y if and only if the pair (x, y) is in the relation.
So, in terms of ordered pairs, the first relation is {(a, a), (a, b), (a, d), (a, e), (b, a), (b, b), (b, d), (b, e), (c, c), (d, a), (d, b), (d, d), (d, e), (e, a), (e, b), (e, d), (e, e), (f, f), (f, h), (f, i), (g, g), (h, f), (h, h), (h, i), (i, f), (i, h), (i, i)}.
Now, can you answer the question romsek asked:
"do you understand what is meant by
reflexive
symmetric
anti-symmetric
transitive? "