All of the other "connections" are historical or cultural. I don't believe you will find original scholarship on the matter, but you can read through history books of organizations and see a few things.
For example, my history book mentions the Alphas assisting the AKAs in a way that is not mentioned in their history book; theirs mentions the possible inspiration/moral support of George Lyle on Ethel Hedgeman at Howard University. Neither book goes so far as to claim a brother/sister relationship. But I have to admit from first hand experience the current international president of AKA seemed to have more "sisterly" sort of interaction with our national president, moreso than the other sorority presidents (as observed at the last two public programs I've attended).
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