Cyclomatic complexity: Difference between revisions

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===Definition===

[[Image:control flow graph of function with loop and an if statement without loop back.svg|thumb|250px|right|A control-flow graph of a simple program. The program begins executing at the red node, then enters a loop (group of three nodes immediately below the red node). On exiting the loop, there is a conditional statement (group below the loop), and finally the program exits at the blue node. This graph has 9 edges, 8 nodes, and 1 [[connected component (graph theory)|connected component]], so the cyclomatic complexity of the program is 9 - 8 + 2*1 = 3.]]

The cyclomatic complexity of a section of [[source code]] is the maximum number of [[linearly independent]] [[path (graph theory)|paths]] within it—whereit—a "linearlyset independent"of meanspaths thatbeing eachlinearly pathdependent hasif atthere leastis a subset of one edgeor thatmore ispaths notwhere inthe one[[symmetric difference]] of thetheir otheredge pathssets is empty. For instance, if the source code contained no [[Control flow|control flow statements]] (conditionals or decision points), the complexity would be 1, since there would be only a single path through the code. If the code had one single-condition IF statement, there would be two paths through the code: one where the IF statement evaluates to TRUE and another one where it evaluates to FALSE, so the complexity would be 2. Two nested single-condition IFs, or one IF with two conditions, would produce a complexity of 3.

Mathematically, the cyclomatic complexity of a [[Structured programming|structured program]]{{efn|1=Here "structured" means in particular "with a single exit ([[return statement]]) per function".}} is defined with reference to the [[control-flow graph]] of the program, a [[directed graph]] containing the [[basic block]]s of the program, with an edge between two basic blocks if control may pass from the first to the second. The complexity '''M''' is then defined as<ref name="mccabe76">{{cite journal| last=McCabe|date=December 1976| journal=IEEE Transactions on Software Engineering|issue=4| pages=308–320|