I checked Reinhard Diestel's textbook on <a href="https://diestel-graph-theory.com/">Graph Theory</a>. p.2 > A graph of order 0 or 1 is called *trivial*. Sometimes, e.g. to start an induction, trivial graphs can be useful; at other times they form silly counterexamples and become a nuisance. To avoid cluttering the text with non-triviality conditions, we shall mostly treat the trivial graphs, and particularly the empty graph, with generous disregard. Only *nonempty* graphs are defined to be connected. (p.9)