Graphs & Trees: Intro

So, what exactly is a directed graph (or a graph, in general?)

A graph (also called an undirected graph) is an ordered pair $G = (V, E)$ in which:

• The set $V$ is a non-empty set of vertices (singular: vertex), also called nodes, and
• The set $E$ is a set of undirected edges of the form $\{v_1, v_2\}$, where $v_1, v_2 \in V$ (each edge connects two vertices.)

Note a graph's edge is a two-way street: having $\{v_1, v_2\} \in E$ is the same as having both $v_1 \rightarrow v_2$ and $v_2 \rightarrow v_1$.