# Do the words 'graphing' a function and 'graph' theory have a common ancestor?

When saying graph in mathematics, it can be either a graph of a function, or a graph in graph theory. However mathematically they have nothing in common. How did they get the same name?

I know graph theory has been invented by Euler (the seven bridges of Königsbergen, 1736), but I haven't been able to find the history of graphing a function. My guess is that Leibniz had done that as well while discovering functions.

Of course, they both have something related to graphical things, but you might as well say that about geometry, topology and often also combinatorics, so that isn't really a statistifactory argument.

How did 'graphing' a function and 'graph' theory get the same name? Was it a confusion, or did they have a common ancestor?

• If you look on the Wikipedia pages for "graph of a function" and "graph theory" and compare the tables of links to the same pages in other languages then you'll see that in most (but not all) languages besides English the term graph for a function's graph and for the combinatorial object are not the same.
– KCd
Jul 10, 2015 at 19:04
• @KCd I'm not sure if I'd agree with that. Dutch ('grafiek' vs. 'graaf'), French ('graphe' vs. 'graphe d'une function'), and German ('Graph' vs. 'Funktionsgraph'). Chinese (函数图形 vs.图, where 函数 means function), which is You see, the words have just the word for function added. Jul 10, 2015 at 19:12
• I was not counting the examples with the word function in them. Though why do you single out Dutch as an example of that? I do not know Dutch, but grafiek and graaf do not involve the word for function (functie).
– KCd
Jul 10, 2015 at 19:46
• For history of function graphs see hsm.stackexchange.com/questions/2378/… and dam.brown.edu/people/mumford/beyond/coursenotes/2006PartIb.pdf Jul 11, 2015 at 0:58
• @KCd No, that was just an example of the similarity between them. Jul 18, 2015 at 19:19