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'I met your parents a week ago before the graduation ceremony.'

I would like to know when the 'before the graduation ceremony' is. I know that we should consider the contexts first, but excluding them, I would like to know if the 'before the graduation ceremony' can be any days of the week before a speaker says or it should be the same day with a week ago. For example, let's assume Today is Monday and of course, a week ago is also Monday, and then the graduation ceremony also should be on late Monday or any days of the week before a speaker says the sentence? I know that it is a really silly question but sometimes this kind of question really drives me crazy and changes my life. Please help me and tell me your opinions. Thank you so much all!!
Comments  
A comma would help clarify:

I met your parents a week ago, before the graduation ceremony.

It does not tell us precisely when the ceremony was, nor even when the meeting was. All we know is that the meeting happened shortly before the ceremony about 7 days ago.
Thank you for the clear and quick answer and so we do not need to see it as the same day with a week ago 100%? Emotion: big smile Am I right?
Students: We have free audio pronunciation exercises.
You are right.
I suspect you meant "I met your parents a week before the graduation ceremony." The "ago" changes everything, and Mister M answered for that.

"A week before the graduation ceremony" does not necessarily mean exactly seven days before. It means "about a week before". If you want it to mean that if the ceremony was on a Monday, you met them on the previous Monday, "one week" is what you want, "exactly one week" is better, and "seven days" is best.
Mister MicawberYou are right.
I am really really sorry about dragging this question out but I am seriously confused now with this question. So what you meant is that a comma is definitely needed, not optional and there is a meaning difference with or without a comma in the example? So without a comma , it is the same date 100%? I don't think you meant this, right? I really hope to hear from you again. Thank you so much as always!!
Students: Are you brave enough to let our tutors analyse your pronunciation?
The comma is optional. I added it for clarification, as I said: my idea was to separate the two time units, that is all.
Anonymous'I met your parents a week ago, before the graduation ceremony.'
I like Mr. Micawber's addition of the comma. The before-phrase only specifies with (slightly) more accuracy the expression a week ago.

I read it thus: The graduation ceremony was a week ago. I met your parents there -- on the occasion of that ceremony, or more specifically, just before it started.

I imagine people gathered and socializing as they begin to take their places for the ceremony which is soon to begin, and during this preliminary gathering and assembling for the ceremony, "I" was introduced to "your" parents.

CJ