To understand Cyclomatic Complexity , lets first understand -

### What is Software Metric?

Measurement is nothing but quantitative indication of size / dimension / capacity of an attribute of a product / process.

Software metric is defined as a quantitative measure of an attribute a software system possesses with respect to Cost, Quality, Size and Schedule.

Example-

Measure - No. of Errors

Metrics - No. of Errors found per person

### What is Cyclomatic Complexity?

Cyclomatic complexity is a software metric used to measure the complexity of a program. These metric, measures independent paths through program source code.

Independent path is defined as a path that has atleast one edge which has not been traversed before in any other paths.

Cyclomatic complexity can be calculated with respect to functions, modules, methods or classes within a program.

This metric was developed by Thomas J. McCabe in 1976 and it is based on a control flow representation of the program. Control flow depicts a program as a graph which consists of Nodes and Edges.

In the graph, Nodes represent processing tasks while edges represent control flow between the nodes.

## Flow graph notation for a program:

Flow Graph notation for a program is defines . several nodes connected through the edges. Below are Flow diagrams for statements like if-else, While, until and normal sequence of flow.

**Mathematical representation: **

Mathematically, it is set of independent paths through the graph diagram. The complexity of the program can be defined as -

V(G) = E - N + 2

Where,

E - Number of edges

N - Number of Nodes

V (G) = P + 1

Where P = Number of predicate nodes (node that contains condition)

Example -

i = 0; n=4; //N-Number of nodes present in the graph while (i<n-1) do j = i + 1; while (j<n) do if A[i]<A[j] then swap(A[i], A[j]); end do; i=i+1; end do;

Flow graph for this program will be

**Computing mathematically, **

- V(G) = 9 - 7 + 2 = 4
- V(G) = 3 + 1 = 4 (Condition nodes are 1,2 and 3 nodes)
- Basis Set - A set of possible execution path of a program
- 1, 7
- 1, 2, 6, 1, 7
- 1, 2, 3, 4, 5, 2, 6, 1, 7
- 1, 2, 3, 5, 2, 6, 1, 7

## Properties of Cyclomatic complexity:

Following are the properties of Cyclomatic complexity:

- V (G) is the maximum number of independent paths in the graph
- V (G) >=1
- G will have one path if V (G) = 1
- Minimize complexity to 10

## How this metric is useful for software testing?

Basis Path testing is one of White box technique and it guarantees to execute atleast one statement during testing. It checks each linearly independent path through the program, which **means number test cases, will be equivalent to the cyclomatic complexity of the program. **

This metric is useful because of properties of Cyclomatic complexity (M) -

- M can be number of test cases to achieve branch coverage(Upper Bound)
- M can be number of paths through the graphs.(Lower Bound)

Consider this example -

If (Condition 1) Statement 1 Else Statement 2 If (Condition 2) Statement 3 Else Statement 4

Cyclomatic Complexity for this program will be 9-7+2=4.

As complexity has calculated as 4, four test cases are necessary to the complete path coverage for the above example.

## Steps to be followed:

The following steps should be followed for computing Cyclomatic complexity and test cases design.

**Step 1** - Construction of graph with nodes and edges from the code

**Step 2** - Identification of independent paths

**Step 3 **- Cyclomatic Complexity Calculation

**Step 4 **- Design of Test Cases

Once the basic set is formed, TEST CASES should be written to execute all the paths.

## More on V (G):

Cyclomatic complexity can be calculated manually if the program is small. Automated tools need to be used if the program is very complex as this involves more flow graphs. Based on complexity number, team can conclude on the actions that need to be taken for measure.

Following table gives overview on the complexity number and corresponding meaning of v (G):

Complexity Number | Meaning |

1-10 | Structured and well written code High Testability Cost and Effort is less |

10-20 | Complex Code Medium Testability Cost and effort is Medium |

20-40 | Very complex Code Low Testability Cost and Effort are high |

>40 | Not at all testable Very high Cost and Effort |

## Tools for Cyclomatic Complexity calculation:

Many tools are available for determining the complexity of the application. Some complexity calculation tools are used for specific technologies. Complexity can be found by the number of decision points in a program. The decision points are if, for, for-each, while, do, catch, case statements in a source code.

Examples of tools are

- OCLint - Static code analyzer for C and Related Languages
- devMetrics - Analyzing metrics for C# projects
- Reflector Add In - Code metrics for .NET assemblies
- GMetrics - Find metrics in Java related applications
- NDepends - Metrics in Java applications

## Uses of Cyclomatic Complexity:

Cyclomatic Complexity can prove to be very helpful in

- Helps developers and testers to determine independent path executions
- Developers can assure that all the paths have been tested atleast once
- Helps us to focus more on the uncovered paths
- Improve code coverage
- Evaluate the risk associated with the application or program
- Using these metrics early in the cycle reduces more risk of the program

## Conclusion:

Cyclomatic Complexity is software metric useful for structured or white box testing .It is mainly used to evaluate complexity of a program. If the decision points are more, then complexity of the program is more. If program has high complexity number, then probability of error is high with increased time for maintenance and trouble shoot.