AFAIK resources need to be within five tiles to link to a city and gain benefit from any % improvements, or to allow training of special units for the diplomacy tech resources.
So what's a tile? The cloth map makes it look like a Shrill Hive I developed is just one 'tile' away from my capital, if tiles are marked by the heavier lines and the dashed lines as opposed to the lines that appear when Show Grid is enabled.
Corollary question: Why would the game let me spend 200 gildars on a site that ends up being "Not linked." Shouldn't I be unable to invest until a link is possible?