Assume two entities, A and B.
M:M relationship exists between entity A and entity B when each occurrence of entity A is related 0, 1, or many occurrences of entity B and each occurrence of entity B is related to 0, 1, or many occurrences of entity A.
Somewhat more formally, Date defines
M:M relationships as follows: “Let A and B be sets, not necessarily distinct. Then a many-to‑many correspondence from A to B is a rule that pairs each element of A with at least one element of B and each element of B with at least one element of A. Equivalently, we might just say the many-to-many correspondence is that pairing
itself.” (2006, page 17).
M:M relationships are commonly seen in real world situations.
M:M relationships are graphed as follows: