The 27-year-old - a deadline day signing - did not make his first start for the club until the 2-1 defeat to West Brom on Saturday, and now he wants to forge a partnership with Fletcher.
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"He has brought me in and I want to play, Steven wants to play and so does everyone else.
"It is up to us to train hard and build on relationships in the team and see where it takes us. If we get a run of games going together I'm sure we will get goals.
"We want to get back to winning ways and we need to pick up points and give the fans a performance they have deserved over the last few weeks."
The Black Cats have lost their last their last three games, a slump that has seen them drop to 15th in the table - five points above the relegation zone.
However, Graham is confident his new club can put daylight between themselves and the bottom three.
He added: "We haven't won in three, but the fans have been right behind us. They've been superb and we'll need them from now until the end of the season.
"We've got 10 games to get as many points as we can and we're focused on looking up to where we could go rather than over our shoulders."