Term to describe the relationship between two people when they share an Alma Mater

Is there a Term to describe the relationship between two people when they share an Alma Mater?

For example; Neil Armstrong is an alumnus of Purdue University. I am an alumnus of Purdue University. Both Neil and I are alumni of Purdue University, which is to say we share an alma mater. So, I'm looking for a term to describe my relationship to to Neil with out needing to explicitly reference the university. Is co-alumni a real term? Is it appropriate to say that Neil and I are co-alumni? Is there something better? Further, is there a way to specifically describe the relationship between two people from the same graduating class?

Thank You in advance!

In this situation I've always heard "fellow alumnus" to describe someone who has graduated from the same university as somebody else.

Fellow adjective
belonging to the same class or group; united by the same occupation, interests, etc.; being in the same condition

Alumnus noun
a graduate or former student of a specific school, college, or university.

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"Fellow alumnus" and "Fellow alumni" get 51100 and 402000 google hits respectively, so they're not completely uncommon phrases. I found it difficult to find a decent definition of the phrase though. It is possible that some people would interpret "fellow alumnus" to mean someone who graduated from the same class in the same year, rather than just the same university in any year.

Note: "alumnus" is the male singular, "alumna" is the female singular, "alumni" is the male/mixed plural, and "alumnae" is the female plural. Informally "alum" and "alums" are sometimes used as gender neutral alternatives.

People who went to the same school as you, even during a different year, are often described as "fellow alumni". A couple of uses:

How to find and reach out to fellow alumni:

We all know that our fellow alumni can be great networking resources. After all, you’ve already got a built-in connection with these folks, no matter what year they graduated.

Alumni networking rules:

If you’ve never met someone before and they’re a high-ranking officer where you want to work, then simply being a fellow alum is way too much of a stretch to be calling on them...

For "someone who graduated the same year as someone else", I would use classmate in North American English. From the OED:

classmate, n. A fellow member of a class at school, college, or university; (N. Amer.) a member of the same graduation class.

Note that this usage is somewhat ambiguous, as one can also be a "classmate" by taking a class with someone. Usually this ambiguity can be resolved by context, since (IMO) it is unusual to call someone a "classmate" in sense of "someone who took a class with me" after that class is over. If someone says "We were classmates at Brown", it usually implies the "same graduating class" sense of the word.