Cruncher is quite correct and I'm afraid bellabee has completely misunderstood the point of my post. There is no mathematical knowledge whatsoever required to solve this puzzle, although doubtless the puzzle was inspired by mathematics and created by a mathematician. The only knowledge of graph theory which I personally possess is the bit I read in the preamble, plus extra interesting but unhelpful stuff acquired while - idiotically - perusing the web looking for help with the final step. Then I realised I was being daft.
Ask yourself exactly what knowldege of "graph theory" you actually applied to solve the fiinal step and I think you'll agree.
I'm not aware of any "number/words" division in the Listener - there have been many excellent puzzles which combine the two - this was an excellent puzzle and very tough, but I don't think one can class it as one of those "hybrids". .
I think the reason that the failure rate for pure number puzzles is lower is because there are fewer opportunities for error, as a rule, the solving process being one of logic and with fewer extra steps, added bars , highlightings etc etc.