According to Real Time Trains, this morning's (and yesterday's and Monday morning's) Glasgow portion ran early. The CS website says the train is booked to arrive at Edinburgh at 03.54 and Edinburgh passengers (who presumably travel in the Glasgow portion) must vacate their berths (or seats) by 05.30, and the Glasgow portion is booked to leave Edinburgh at 05.44 but actually left at 05.10 on Monday, 04.22 yesterday and 05.19 today. I'm guessing that this was because there were no Edinburgh passengers so it was decided to let the Glasgow portion run early rather than have it taking up platform space at Waverley.The Glasgow and Inverness portions are joining at Edinburgh. Passengers from Edinburgh can join there. It will then run as one combined train to Euston in the highlander path.
Only the Fort William and Aberdeen portions are completely cancelled. Glasgow has revised timings; Edinburgh is just using the Glasgow coaches (so late boarding / early alighting) and Inverness is unchanged. It is using the highlander path from Edinburgh to London (and vice versa).