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?
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.