The Shrewsbury projectWhich links hold Shrewsbury together? A graph project on real streets
Count the separate pieces with union-find, close the river bridges, then find the links a graph algorithm calls bridges.
An OpenStreetMap API download covering central Shrewsbury provides the raw material, with every road, path and footway kept at full detail: 6,308 points joined by 6,971 links. The River Severn's centre line comes in the same download. A little geometry finds the bridge links whose line crosses the river: ten of them. Nine connect the part of the network holding the town centre to the other side: Welsh Bridge, English Bridge, Kingsland Bridge, Greyfriars Bridge, Frankwell Suspension Bridge, Porthill Footbridge, Castle Walk Footbridge and two unnamed footway links a few metres apart. The tenth, an unnamed service link, crosses the river line but only touches a few stray points.
To count how many separate pieces a network has, the program uses union-find, also called a disjoint-set structure. Every point starts in its own group, and each link merges the two groups it joins; with a trick called path compression, asking "which group is this point in?" stays fast even for thousands of points. Before anything is closed, the download already holds 11 pieces, because the edge of the rectangle chops off a few fragments, and the main piece has 6,206 points.
Closing crossings on the mapped Shrewsbury network, computed in Python from OpenStreetMap data on 29 September 2026| Closure test | Outcome |
|---|
| Nothing closed | Main piece of 6,206 points |
| Any single river crossing closed | Town centre still joined to the rest |
| All ten crossings closed | Town-centre piece of 3,582 points, other side 2,619 |
| Graph-theory bridges in the whole network | 1,621 of 6,971 links |
| Largest piece any one link can cut off | 104 points |
Closing any single river crossing leaves the town centre connected, because the others take over. Only when all ten are closed does the network split, into a town-centre piece of 3,582 points and another of 2,619. That is redundancy, and it is exactly what engineers want from roads, power lines and computer networks alike.
Then comes the twist. In graph theory a "bridge", or cut edge, is any single link whose removal splits the network, found here with Tarjan's algorithm in one pass. There are 1,621 of them, nearly a quarter of all links, yet not one is a river bridge. Most lead into dead ends or short spurs: 564 cut off a single point, 877 cut off between two and nine, and the most any one link can isolate is 104 points. The river bridges, the famous ones, are precisely the links the network can survive without.
Ages 8 to 11
Draw a small town as dots and lines, then rub out one line at a time and see what gets cut off.
Ages 11 to 15
Load a street network in Python and count its separate pieces with union-find.
Ages 15 and up
Code Tarjan's algorithm, find every cut edge and test which closures split the town.
OpenStreetMap data, our graph
Street and river data is from OpenStreetMap and its contributors under the Open Database Licence. The graph, the closures, the union-find counts and the cut-edge analysis are our own work, and they describe the mapped network inside one rectangle, not official road plans.
