I will mostly focus on American English, since the expression graduated from college is not used in the same sense in the UK.
I doubt there are any contexts where, in American English, one of the sentences
[1] i Has your brother graduated from college?
ii Did your brother graduate from college?
would be acceptable but the other would not. Having said that, one or the other may be preferred.
In brief, the simple preterite [1ii] is used in practice much more frequently. Having said that, there may be some circumstances, namely those where 'the focus is on the present' (in an appropriate sense), where the present perfect is more likely than in other circumstances. This is discussed in the section 'A general consideration', below.
Evidence from various corpora
Evidence from the Google Books Ngram Viewer and COCA
Interestingly, if you search Hoogle Ngram Viewer, you will find that [1i] has no hits at all. Similarly, on the Corpus of Contemporary American English (COCA) there are zero hits for 'have you graduated', but 8 hits for 'did you graduate', including entries such as
Have you ever had a job? Did you graduate from high school?
Did you graduate from Paseo, Miss Bloom?
"So did you graduate?" I ask.
Evidence from Google Books
If one searches google books, one does find a number of hits for both 'have you graduated from' and 'did you graduate from', though the latter are more numerous.
Apart from the overall higher number of hits for the simple preterite 'did you graduate from', there is one other tendency that seem to be discernable.: if a specific institution is named (as in, Did you graduate from Gibbs High School?), then the simple preterite is strongly preferred. (Obviously, if a specific time is indicted or asked for, then the simple preterite is basically obligatory, as in What year did you graduate from college?)
A general consideration
It is not easy, when searching on Google Books, to precisely specify the context for an expression, and so I will add something that comes close to being a mere opinion. However, this opinion is at least consistent with the general analysis from CGEL reproduced below.
The general observation is that the present perfect (as in [1i]) is used when 'the focus is on the present'. This focusing may take several forms. Perhaps we are focusing on the fact that the graduation is recent; one way to emphasize that focus even more would be to add yet (Has your brother graduated from college yet?).1 . Or, perhaps we are focusing on the fact that the graduation had a specific result—your brother becoming a college graduate—which persists through and is relevant now.
1In some varieties of American English, even the presence of yet wouldn't exclude the use of the preterite:
%Did your brother graduate from college yet?
(Here ' % ' in front of a sentence signifies that what follows is grammatical only in some dialects.)
On the other hand, if the focus is on the past, then the simple preterite is more likely. This helps explain the observation, noted above, that the simple preterite is preferred when a particular institution is specified. Note that if the institution is famous, so that becoming a graduate of that particular institution is itself a well-recognized change in status, then the present perfect becomes more acceptable. For example, it is easier to imagine contexts where Have you graduated from Harvard? is acceptable2 than it is to imagine contexts where Have you graduated from Lincoln High School?3 is acceptable.
2One example would be the contexts where what you're really asking is Have you graduated from an elite university?
3Lincoln is one of the more frequent names of high schools.
So suppose the institution itself is not famous, and the graduation did not happen recently. Then the fact that one graduated from a specific high school or college is not connected to the present in a way that would warrant the present perfect. This is arguably so even when the identity of the institution is actually relevant to the present situation in some other way. An example: You seem very familiar. Did you attend Lincoln High School? Here it does matter right now whether the person attended that specific high school. But since the relevance concerns neither recency nor change in status, we are more likely to stick with the simple preterite. (The present perfect is also possible, but is less likely.)
General analysis from CGEL
For completeness, it will be helpful to recall the main uses of the present perfect. This discussion follows (and quotes) that in CGEL, pp. 143–146.
In the first place, there is a reasonably sharp distinction between continuative and non-continuative uses. A useful criterion is whether the expression in question is compatible with ever since: if it is, the use is continuative; otherwise, it is non-continuative. In your example, we clearly couldn't add ever since (as in *Has your brother graduated from college ever since?, where the ' * ' in front of a sentence signifies that what follows is not acceptable English). Thus your sentence is an example of non-continuative use. Further, within the category of non-continuative use, traditionally there are three further subdivisions: the experiential (or 'existential') perfect, the resultative perfect, and the perfect of recent past. These three are not as sharply delineated, and many examples of use belong to more than one subdivision. Nevertheless, grammarians consider the distinctions useful. Let's consider how they might apply to [1i].
The experiential perfect
This subdivision has to do with 'the occurrence of situations within the time-span up to now'. CGEL gives three types of use that belong to this subdivision, of which the most relevant for us is exemplified by
[11] iii His sister has been up Mont Blanc
twice.
The connection with now is less direct in [11iii]: the ascents could
be quite a long time in the past. The focus, however, is not on their
occurrence at some particular time in the past but on the existence of
the situation within the time-span. The connection with now is the
potential for occurrence, or recurrence, of the situation at any time
within the time-span up to now. Thus [iii] implicates that his sister
is still alive, while I haven't been to the market yet implicates
that the possibility of my going to the market still exists (it hasn't
closed down).37
37The implicature may be weaker: that the same kind of
situation is still possible. Nixon has been impeached, for example,
can still be acceptable even though Nixon has since died, given a
context where the issue is the occurrence within the time-span of
situations of the kind 'impeachment of a president'.
Given that one graduation from college is usually a one-time thing, this subdivision seems to not fit very well with [1i]. I'm not saying it's impossible to interpret [1i] as an experiential/existential perfect, but only that it is less likely than the alternatives.
The experiential/existential perfect vs. the simple preterite
The experiential/existential perfect can be usefully contrasted with the simple preterite in the following situations (and unlike some other cases, this contrast is present in all varieties of English). This will be useful to review, despite the fact that we decided that [1i] is less likely to be interpreted as experiential/existential perfect.
[12] i a. It is better than it has
ever
been. b. It's
better than it was.
ii a. Have
you seen
Jim? b. Did
you see Jim?
In [ia] the comparison is between its quality now and its quality at
any time within the time-span – clearly the potential for it to be of
such and such a quality still exists. In [ib] the comparison is between
now and then; the past is contrasted with the present, the 'then'
situation is over and excludes now.
Example [i2iia] brings out the point that there may be limits to the
time-span beyond those inherent in the situation itself. The inherent
limit is that Jim (and you) must be alive, but in the salient
interpretation I will have in mind a much shorter span than this: the
time of his current visit to our vicinity, today, the period since we
were last together, or whatever it might be. It would not be
acceptable for you to answer yes on the strength of having seen him
before this time-span. Whatever the limits on its beginning, however,
the time-span stretches up to now. But [iib] is very different.
Assuming again that you know Jim and have seen him perhaps many times,
you need to determine more specifically what I am asking. This time,
however, it is not a matter of placing limits on the start of the
time-span up to now, but of finding which particular, definite past
time I am asking about - your visit to Jim's sister last month, or
whatever it might be, but a time that is over, exclusive of now.
The resultative perfect
CGEL again lists three types of use that belong to this subdivision. The most relevant for us seems this one:
[14] i She has broken her
leg. He has closed the
door. They've gone away.
The clearest cases of the resultative perfect are illustrated in [i],
where the situation is one that inherently involves a specific change
of state: breaking a leg yields a resultant state where the leg is
broken, closing the door leads to the door's being closed, going away
(from place x) results in a state where one is no longer at place
x, and so on. The connection with the present in this resultative use is that the resultant state still obtains now. She has broken her
leg does not mean "Her leg is broken", but this is the likely
implicature unless the context selects an experiential interpretation.
Cases like [i] are known more specifically as the perfect of
continuing result: the resultant state begins at the time of occurrence of the past situation itself and continues through into the
present.
This fits quite well with [1i]: the resultant state is 'being a college graduate' (or 'having a college degree'), which begins at the time of occurrence of the past situation itself (at the time of graduation) and continues through into the present.
The perfect of recent past
[15] i It has been a bad start to the year with
two fatal road accidents overnight.
ii I've
discovered how to mend the fuse.
iii She
has recently/just been to Paris.
One respect in which a past situation may be connected with now is
that it is close in time to now. It is clear from examples like
[11iii] (His sister has been up Mont Blanc twice) that it does not
have to be recent, but there is nevertheless a significant correlation
between the present perfect and recency, whereas the simple preterite
is quite indifferent as to the distance between Tr and
To. [Here Tr is the 'time referred-to', the time when the action is taking place, e.g. the time of graduation in [1i]. To is the 'time of orientation', the time relative to which we are positioning Tr as being before, simultaneous, or after it; in [1i], To is the time of utterance, 'now'.] The present perfect is therefore the one most
frequently used in news announcements, as in the radio bulletin
example [15i]. It is arguable that the experiential and resultative
categories are broad enough to cover all non-continuative uses, but
recency adds an important component to the account. For example,
[15ii] has a continuing result interpretation: the discovery resulted
in my knowing how to mend the fuse and this knowledge persists. Such
knowledge can persist for a long time, so there is nothing in the idea
of continuing result itself to exclude my having made the discovery
years ago. But in fact the normal interpretation involves a recent
discovery. We have noted that experiential perfects like [i2iia] (Have you
seen Jim?) impose limitations on the time-span up to now beyond those
inherent to the situation, and these additional limitations also
involve recency.
Thus, [1i] is likely to be interpreted as asking whether the brother has graduated from college recently. The addition of yet would further emphasize this connotation.