The Scotland midfielders were peripheral at times last season but will both be given the opportunity to earn lead roles in the squad under their Scottish coach.
Irvine was appointed on Sunday and has acknowledged that has been impressed by what he has learned about the Scots in his squad. "They are both very good players," said Irvine, who had been working in Everton's academy.
"I have followed their careers, especially James. I was at Newcastle United when he was coming through at Middlesbrough. Graham is one I've admired since he first came and played at Championship level. They are both very good players."