M2, M4, M6, M8, Motorway!

I've always* wondered how far it was possible to go staying only on consecutively numbered motorways in the UK. I've also been looking for a reason to fiddle around with Graphviz since the eternally helpful Colin Wright pointed me towards it a while ago.

So I found a database of the UK's motorways and created a graph:

Graph generated using

Labelled nodes represent the motorways themselves and edges represent a shared junction between two motorways. It strikes me that this is almost exactly opposite to the way that motorways actually work.

From this diagram, it appears that the answer to my original question, "how far is it possible to go staying only on consecutively numbered motorways in the UK?", with the further refinement that "far" means the number of motorways experienced rather than an actual distance, is rather more boring than I was hoping for.

Unless I've missed something (please correct me if so) it appears to be...

... wait for it...

Photo by Jack Hunter on Unsplash

That is:
 M4 Motorway , M5 Motorway , M6 shield.

Sorry, folks.

Another interesting** thing that pops out of the graph above is that there are no disconnected subgraphs: it's possible to visit all of the UK's named motorways without spending time on a road that isn't a motorway.

What else have I missed? Can anything interesting be gleaned from the graph above? Does anyone have an ideas about how it could be used educationally? Are there any questions (deep, shallow, important or who-cares) that might be clarified by such a graph?

* Well, not always, but, y'know.
** To me, that is. If you find it interesting too, I'm chuffed to bits. If you don't, I don't need to hear about it thanks. What are you even still doing here?

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