The ex-Edinburgh Gunners chief subsequently guided the Scots to wins over the Barbarians and Romania in the summer to stake his claim for the job.
Now former Scotland prop Graham believes the series against Argentina, Samoa and New Zealand next month will see a new dawn emerge for the national team.
He said: "We have to be exciting.Â You have to be excited to play for your country.
"You have to want to play for your country and enjoy what you are doing and that's certainly been reflected in training.
"We're not going to hide from the challenge. We are not going to skirt around whatever the opposition are going to throw at us.
"We're going to have a go and bring back the passion of playing for Scotland."
Williams was axed from his position in March amid speculation of growing dressing room unrest.
But Scotland assistant coach Sean Lineen is looking for players to enjoy training again under Hadden.
He said: "We want players to enjoy coming to training - to come to train with a smile on their face, not doing it as a chore.
"Frank has created an environment where he does not want the backs to take a back seat.Â He wants them to be right up there performing."