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I understand what cyclomatic complexity is, but I was trying to find the origin/meaning behind the word "cyclomatic" and could not find anything that wasn't about cyclomatic complexity. Does this word exist outside of this phrase?

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    If read the Wikipedia article completely, you find the explanation. It refers to the so-called cyclomatic number (the minimum number of edges that must be removed from the graph to break all its cycles), also know as circuit rank. Oh, and the downvote button here says "this question does not show any research effort", so do not be astonished if you get some downvotes for not looking at Wikipedia. – Doc Brown May 26 '16 at 20:41
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    Is the Wiktionary definition of cyclomatic helpful enough? – Vincent Savard May 26 '16 at 20:41
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While the Wikipedia article goes into great detail about the maths and implications of "cyclomatic complexity", I don't think it adequately explains the word "cyclomatic".

The description of the cyclomatic number offered by Doc Brown's comment "the minimum number of edges that must be removed from the graph to break all its cycles" is great if you're a mathematician - but not all programmers are (I did some engineering mathematics, but graph theory is way beyond my experience in maths).

Luckily, the wiktionary helps with more descriptions:

(computing, programming) Of or relating to a software metric that measures the complexity of a program based on the number of linearly independent paths through the source code.

So - it's been co-opted from maths into networking and programming to act as an indicator of software complexity by describing the number of branching points through a given program or function.

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