The Highland neighbours have both reached national finals, with Inverness winning the Scottish Cup last season and suffering defeat by Aberdeen in the previous year’s League Cup final.
Ross County, for their part, stormed past Celtic and Hibs while still a First Division club only to be beaten in the 2010 Scottish Cup final by Dundee United.
Graham sees no reason, given the neighbours’ success, why County cannot go all the way themselves.
The former Dundee United and St Johnstone striker, a beaten Scottish Cup finalist with United in 2014, said: “The two clubs are similar in size and fan-base and Inverness won one of the biggest competitions in Scotland last year.
“So to see them achieve it probably does give everyone at our club a wee edge and think ‘why can’t a club like Ross County do it?’
“County did reach a Scottish Cup final in 2010 but it wasn’t to be that day, so hopefully we can do it this season.
“At the start of the season we set to finish in the top six and to get a good cup run.
“When you get into a quarter-final, you’re thinking to yourself ‘we can probably go and win this’.
“Obviously, you need a bit of luck, as anything can happen on the night in cup competitions. Hopefully that luck can shine on us.”
Graham tasted defeat in his first Highland derby before the international break, but insists that game will not be playing on Staggie minds tonight.
The 27-year-old stressed: “It should be exciting. It will be played to a finish on the night, so it will be a good old-fashioned cup-tie.
“They came here and beat us 2-1 last time, but it’s a cup competition and we’ll probably not think too much about that.”