I came across an issue with the definition of a (directed) graph in Sipser's Introduction to the theory of computation, 2nd Ed.
On pp.10, An undirected graph, or simply a graph, is a set of points with lines connecting some of the points. The points are called nodes or vertices, and the lines are called edges, ...
On the same page,
No more than one edge is allowed between any two nodes.
If it has arrows instead of lines, the graph is a directed graph,...
In Figure 0.16 on pp.12, there is an example of a directed graph, an arrow from node 1 to node 2 and an arrow from node 2 to node 1.
So, we have two arrows in opposite direction between two nodes.
I understand all of these basics.
My question is,
Is directed graph a graph?