The A1: the centre of the UK road network

Continuing the driving theme from last week, I looked into the connectivity of roads in the UK.

You may have heard of Six Degrees of Kevin Bacon, a game where you try to get from any film actor to Kevin Bacon in six steps or less by going through actors who have been in a film together.

The game suggests that there is an actor at the “centre” of the movies - someone who has had a long and varied career, and is most closely connected to all other actors. It’s not actually Kevin Bacon, and in fact the actor at the centre changes, since new movies are made all the time. There’s a good discussion of who is at the centre of the “Hollywood universe” on Wikipedia.

My idea was to treat the UK’s network of motorways, A roads, and B roads as a graph and to try and find its “centre” using the same techniques as those used to find the centre of the movie universe.

The A1, which connects London to Edinburgh, is the road at the “centre” of the UK’s road network. The image shows all the roads that share a junction with the A1.

(The interactive version allows you to hover to see each road’s connections.)

In this analogy, the graph’s nodes are roads, and its edges are made up of connections between roads - that is, whenever two roads meet at a junction. (So roads are “actors”, and junctions are “films” in the movie analogy.)

Note that this graph is exactly the opposite of the way we usually think of road networks, where nodes are junctions and edges are roads. It also discards geography in the sense that the spatial order or layout of junctions are irrelevant: all that matters is if two roads meet somewhere. We can use this graph to find the minimum number of roads we need to travel on to get from one road to another - this is not the shortest path in terms of distance however!

If we look simply at the number of connections (junctions) each road has, we find that the A1 is not actually the most connected road in the UK:

A6: 172
A38: 150
A1: 132
A5: 130
A40: 125
...

However, this doesn’t take into account roads that act as “hubs” to connect roads from different parts of the network to each others. For that, there are various “centrality” measures, including betweenness centrality and closeness centrality. On these two measures, the A1 scores the highest, and for this reason can be said to be at the centre of the UK road network.

I won’t explain what these measures mean here, for that I highly recommend Who is the Centre of the Movie Universe? by Rhyd Lewis, which also has Python code that I used to base my analysis on.

Visualization type: network graph

Data source: OS Open Roads (GeoPackage, 888 MB, compressed)

Technical notes: generated using NetworkX, Cytoscape.js, and d3; code