# Cyclomatic complexity

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It is the complexity calculated based on the number of paths through the code.

Every program encompasses statements to execute in order to perform some task and other decision-making statements that decide, what statements need to be executed. These decision-making constructs change the flow of the program.

The metric itself is based on graph measures on the control flow graph of a method and describes the non-linearity of this graph. For structured programming the metric is roughly equivalent to one plus the number of loops and if statements. The decision-making constructs used to create the graph model are IF-ELSE, DO-WHILE, WHILE, FOR, TRY-CATCH, GOTO, \$CASE and \$SELECT statements, and postconditionals like GOTO:pc, SET:pc, etc.

Each function has a minimum complexity of 1.

If we compare two programs of same size, the one with more decision-making statements will be more complex as the control of program jumps frequently.

## Method of calculation

Process to make flow control graph:

• Break program in smaller blocks, delimited by decision-making constructs.
• Create nodes representing each of these nodes.
• Connect nodes as follows:
• If control can branch from block i to block j ⇒ Draw an arc
• From exit node to entry node ⇒ Draw an arc

To calculate Cyclomatic complexity of a program module, we use the formula

```V(G) = e – n + 2
```

Where
e is total number of edges
n is total number of nodes

Check the next example:

 Code Flow Chart Flow Graph → → The Cyclomatic complexity of the above module is

```e = 10
n = 8
Cyclomatic Complexity = 10 - 8 + 2
= 4
```

## History

Cyclomatic Complexity is a metric that was introduced by Thomas McCabe in 1976 and aims at capturing the complexity of a method in a single number.

Actually, the original publication talks about the more general term module, but today this typically means function or method for most languages.