The most common and most likely answer to this crossword clue is the 11 letter word CORRELATION
I've seen this crossword clue in The Sunday Telegraph
C
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More clues leading to the result CORRELATION
Buddy explains!
The straight part
We know that "Mutual connection" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mutual connection = correlation.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CORRELATION mean?
CORRELATION noun- A reciprocal, parallel or complementary relationship between two or more comparable objects.
- One of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship.
- An isomorphism from a projective space to the dual of a projective space, often to the dual of itself.