The Hinckley projectThe cyclomatic number: counting loops by subtraction
Links, minus points, plus one.
A single OpenStreetMap query returns 1,324 mapped roads in a box around Hinckley, from main roads to residential streets. Joined together, the largest connected piece has 8,524 mapped points and 8,805 short segments between them. Most of those points are just bends. Setting the bends aside leaves the points that matter: 673 dead ends and 1,195 junctions, of which 1,156 are three-way, 38 four-way and one five-way. That makes 1,868 points, and there are 2,149 stretches of street linking them.
Counting loops in the Hinckley street network three ways (our Python run on OpenStreetMap data)| How the network is described | Points | Links | Links - points + 1 |
|---|
| Every mapped point and segment | 8,524 | 8,805 | 282 |
| Dead ends and junctions only | 1,868 | 2,149 | 282 |
| After removing all dead-end branches | 5,196 | 5,477 | 282 |
The answer is 282 every time, and that is the point. Adding a bend to a road adds one point and one link, so the subtraction does not notice. Cutting off a cul-de-sac removes one point and one link, so it does not notice that either. The number only changes when a loop is made or broken. To be sure the formula was not fooling us, the learner asks a graph library to list a full set of independent loops directly, and it returns 282 of them. Seen from the other side: a network with no loops at all, a tree, would need 8,523 of the segments to keep everything joined, and the remaining 282 are the ones that each close a loop.
On a perfectly flat map, 282 would also be the number of enclosed blocks, the patches of land with streets all the way round. Hinckley is not perfectly flat in that sense: 11 of the mapped roads are tagged as a bridge or tunnel, where one road crosses another without joining it. So we describe 282 as the number of independent loops, which is exact, and only roughly as a count of blocks. A second limit: roads leaving the box are cut at its edge and counted as dead ends, which can hide loops that close outside it.
Now the same idea on code. Draw a Python function as a flowchart and every if, every loop and every "and" or "or" adds a branch. McCabe's cyclomatic complexity is the number of independent routes through that chart, and the shortcut is to count the decision points and add one. The learner writes a small tool using Python's ast module and points it at the scripts that did the street analysis. The loop-counting function scores 7 and the branch-peeling function 8. The function that loads the map scores 16. McCabe's paper recommended splitting up any routine that scored above 10, so by our own measure that one deserves splitting, and we say so.
Ages 8 to 11
Draw dots and lines, count both, and check that lines minus dots plus one equals the loops you can see.
Ages 11 to 15
Build the Hinckley network in Python and show that bends and dead ends do not change the answer.
Ages 15 and up
Confirm 282 with a cycle basis, then write a complexity counter and run it on your own code.
Map credit and caveats
Street data (C) OpenStreetMap contributors, under the Open Database Licence, read 30 September 2026. The network, the counts and the complexity scores are our own calculations. The box also takes in ground beyond Hinckley itself, and a different box would give a different number.
