"I'm feeling really good," Graham said. "It's good to be here, obviously."
Graham said he saw a doctor in Minnesota last week after the injury, but tests on the shoulder revealed that his injury wasn't serious and that he'd be able to return this year. Graham is 1-1 with a 5.15 ERA with 47 strikeouts and 17 walks in 57 2/3 innings.
"The doctor checked me out and said it was just a little bit weak and there was a range-of-motion loss," Graham said. "So we've just been stretching that out a lot. So I got some rest and now it's about getting that feel back on the mound. It's nothing serious."
Hughes, meanwhile, is also set to join the Twins on their trip, as he threw his second bullpen session on Sunday, and is scheduled to throw a simulated game in Kansas City on Wednesday. Hughes is on the 15-day disabled list retroactive to Aug. 10, and is expected to rejoin the rotation this month.
Perkins' status remains unchanged, as he's still dealing with a back strain and back spasms. The Twins are waiting for that to calm down before he throws again.
Nolasco, who has been out since June 1 with a right ankle impingement, has been running and throwing without any issues, but time is running out on him to return this season. The Twins haven't fully ruled him out for the year, but he's yet to throw off a mound.
• Top pitching prospect Jose Berrios made his final start of the year at Triple-A on Saturday, and will be shut down for the rest of the season after reaching his innings limit. Berrios, ranked as the No. 22 overall prospect by MLBPipeline.com, posted a combined 2.87 ERA with 175 strikeouts and 38 walks in a career-high 166 1/3 innings between Double-A Chattanooga and Triple-A Rochester. His 175 strikeouts led the Minor Leagues, but Twins general manager Terry Ryan recently said Berrios won't be called up this year.
"I trust his call on it," Twins manager Paul Molitor said. "He's seen enough guys and knows how to protect people. I think everyone tried to imagine [Berrios] coming up here and doing something to help us win games but there's a real possibility he'd be doing something he isn't familiar with. It was really an unknown what we were going to get and we were going to be extending past what we thought was the right amount to pitch this year at his age."
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, follow him on Twitter @RhettBollinger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.