Here's a line from my textbook that I'm having trouble understanding:
Let $G$ be a simple graph with $n$ vertices and $m$ edges. If $G$ is undirected then then $m\leq \frac{n(n-1)}{2}$, and if $G$ is directed, then $m\leq n(n-1)$
Does this mean that if the second condition holds then the graph must be directed even if it was not specified as such?
If this is not the case but the second condition still holds for $G$, can we at least say that $G$ has an Eulerian Cycle if $m$ is even, since we know that when $G$ is directed then: $$\sum_{v \in G}\mathrm{indeg(v)} = \sum_{v \in G}\mathrm{outdeg(v)}=m$$ and this would indicate that $G$ has an even degree?