The graph notation is not fixed thorough this article.
- First we are presented with the notation $G\left(V,E\right)$, which uses the symbol $G$ as a functor to create a graph from two sets $V$ and $E$. As a programmer, this notation is nice because it is akin of how object-oriented programming works.
- Then $H\left(W,I\right)$ implies that $G$ is not a functor at all, but the notation $G(V,E)$ is a mere abbreviation for $G=(V,E)$.
- Finally $G_1=G(V_1,E_1)$ and $G_2=G(V_2,E_2)$ again uses $G$ as a functor.
Even Boundy & Murty (Graph Theory, Graduate Texts in Mathematics, Springer) which notation has become kind of standard, have some difficulty defining what a graph is from a set theoretical standpoint. They say "a graph $G$ is an ordered pair $\left(V(G), E(G)\right)$ consisting of a set $V(G)$ of vertices and a set $E(G)$, disjoint form $V(G)$, of edges, together with an incidence function $\psi_G$ that associates with each edge of $G$, an unordered pair of (not necessarily distinct) vertices of $G$". So that it is an ordered pair with an extra thing outside of that ordered pair. --M. Abarca (talk) 19:37, 21 August 2014 (CEST)
Graph. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Graph&oldid=33049