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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. Even so, we should fix a notation. --M. Abarca (talk) 19:37, 21 August 2014 (CEST)

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