Updated June 13, 2012: Added tags, removing an old link.
There may be a Graham Road today, with a gas station, schools, and lots of businesses, but it's not the same Graham Road of yesteryear. First off, a 1980s aerial picture did show the "multiple segments", and while it crossed the railroad, it did not go to Dowling (which was still one continuous road at the time). Secondly, it was in its "segments". While I couldn't compare aerials, I did find that on a 1990 city report that North Graham was recently extended past Victoria, which means the Castlebrook section was not part of the original Graham segment, and that means Victoria and Arnold were the other Graham segments.
Victoria Avenue between Castlebrook and Arnold, is, of course, a nice two-laned road with turning lanes, wide bike paths, and sidewalks, but Arnold Road is closed to traffic, except for little parts on both ends. The bike "cul-de-sac" at Arnold, as seen behind CSMS is where Old Schaffer intersects, which is mostly closed off to vehicular traffic, continues down to the current Graham Road, which probably continued some way before fizzling out. All this must have changed in the late 1980s, when the streets were added in that area (but no homes), with Graham Road being broken up into segments. This is the era in which the "people names" streets were added, and two of the new segments created from Graham included Arnold and Victoria, both of which were extended. Arnold must have been never improved and abandoned by the early 1990s (a detailed city map in 1994 shows it as "abandoned ROW"), probably around the time of the new junior high. South Graham must have been stubbed out to include Wellborn and the highway. North Graham then was extended to Dowling, cutting the road in two.
The problem is, of course, that's not actually how it turned out: Old Schaffer Road and Graham were not part of the original Graham, as maps show a road coming off of Graham, and bending toward the highway. That is modern-day Old Schaffer Road and Graham, making a right-hand turn that is right across from Cypress Grove.
I don't know the naming history of these roads, I don't know why they called this segment South Graham at all, unless the north end of Graham was always called North Graham Road, which would be odd because they cut off North Graham at Victoria (back when it actually connected to Victoria), and then in the late 1980s, added a segment to the north of it, calling it North Graham Road (again, this is Castlebrook). I've seen on maps that Old Schaffer, that is, the road (I think it doesn't have street sign) was called Schaffer Road, and then, in parenthesis, "E. Graham Road". It's all very confusing. It's possible that in the early days there were two roads: Graham and Schaffer, both out of town farm roads that led essentially nowhere (though Schaffer connected to the highway).
Graham's segments were extended, creating Victoria Avenue (possibly Victoria Road at first), Arnold Road, and North Graham Road. Schaffer's southern segment was extended, creating South Graham Road.
Whatever the case, Old Schaffer is mostly closed save for a drivable part near Cypress Grove (and a bit of Hasselt Loop), North Graham would ultimately be truncated, its railroad crossing and stoplight at Wellborn be completely torn up for suburbia (except for the northern most section, renamed Castlebrook), Rock Prairie extends past Victoria to Gandy (and beyond), and South Graham would get a total rehab, getting bike lanes, sidewalks, concrete, and turning lanes (like Victoria), and be renamed to simply Graham once more (this happened around 2002).
Arnold would become a bike path for most of its right of way.
It was always North Graham that struck a chord with me personally, from fuzzy memories of when it did cross Wellborn, and the great beyond that lay beyond the stoplight (sort of like the "green light" in The Great Gatsby, except in a different context).
I also found a Google Maps Street View picture of the truncation from the other side of Wellborn. This was demolished when Wellborn was widened.
Also, some pictures of the area and how has it changed. From top to bottom, 1995, 2003, 2010.
Here's the North Graham Retail article. It's not yet complete.
As a final word, here's the current ending of North Graham as it ends at Old Wellborn. I've always felt there was something sad about it...