A flow graph 𝐹 with entry node (1) and exit node (11) is shown below: How…

Key idea: the number of regions in a connected flow graph equals its cyclomatic complexity M.

Formula:

• M = E - N + 2 (for a single connected component)

Step 1: Count the nodes (N).

• All numbered nodes from the diagram: 1 through 11, so N = 11.

Step 2: Count the edges (E). List each directed edge shown in the diagram:

• 1 -> 2

• 2 -> 3

• 3 -> 6

• 3 -> 4

• 4 -> 5

• 5 -> 10

• 6 -> 7

• 6 -> 8

• 7 -> 9

• 8 -> 9

• 9 -> 10

• 10 -> 1

• 1 -> 11

Counting the listed edges gives E = 13.

Step 3: Apply the formula.

• M = E - N + 2 = 13 - 11 + 2 = 4

Conclusion: The flowgraph has 4 regions.