Structured Testing - McCabe and Associates

4.2 Counting flow graph regions
When the flow graph is planar (no edges cross) and divides the plane into R regions (including
the infinite region “outside” the graph), the simplified formula for cyclomatic complexity is
just R. This follows from Euler’s formula, which states that for planar graphs n - e + R = 2.
Re-arranging the terms, R = e - n + 2, which is the definition of cyclomatic complexity. Thus,
for a planar flow graph, counting the regions gives a quick visual method for determining
complexity. Figure 4-8 shows a planar flow graph with complexity 7, with the regions numbered
from 1 to 7 to illustrate this counting technique. Region number 1 is the infinite region,
and otherwise the regions are labeled in no particular order.
28
1
2 3 4
5 6 7
Figure 4-8. Planar graph with complexity 7, regions numbered.