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?