The dispute crept into cyberspace Wednesday using the popular Google website as the battleground.
A quick search of "hans island" revealed a paid advertisement with the banner headline: "Hans Island is Greenland. Greenland natives have used the island for centuries."
The ad was linked to the Danish government's foreign affairs web page with the letter condemning Graham's visit.
The advertisement was not a Danish government initiative and whoever placed it was acting alone, Kristensen said.
But that didn't stop one Internet expert - and patriotic Canuck - from striking back.
Toronto resident Rick Broadhead placed a Google ad and said the Canadian government needs to get with the times.
With Ottawa prepared to spend billions to boost its military presence in the Arctic over the coming years, he said an Internet campaign is a dirt-cheap way to spread Canada's argument.
"Eight cents per click - or $200 a month - is money well spent to assert our sovereignty in the North," said Broadhead, who has written extensively about the Internet.
"Political battles are not fought solely in the press these days. They're fought on the Internet as well."
Broadhead's website includes a fluttering Maple Leaf flag and outlines Canada's traditional argument that Hans Island belonged to the British and became Canada's in 1867.
The Danes say it is closer to Greenland than Canada and is therefore Danish soil.