The most common and most likely answer to this crossword clue is the 5 letter word CHART
I've seen this crossword clue in The Times
C
H
A
R
T
More clues leading to the result CHART
Buddy explains!

The straight part
We know that "graph" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case graph = chart.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 CHART mean?
CHART noun- A map.
- A systematic non-narrative presentation of data.
- A written deed; a charter.
- A subspace of a manifold used as part of an atlas
- To draw a chart or map of.
- To draw or figure out (a route or plan).
- To record systematically.
- (of a record or artist) To appear on a hit-recording chart.