Formal Notation

Mathematicians write a graph as $G = (V, E)$ where $V$ is the set of vertices and $E$ is the set of edges. For example, $V = \{1, 2, 3\}$ and $E = \{(1,2), (2,3)\}$.

An edge $(u, v)$ means there is a connection from vertex $u$ to vertex $v$. In an undirected graph, $(u, v)$ is the same as $(v, u)$.

You will see this notation in textbooks and research papers. I'll use plain English most of the time, but knowing the formal notation helps when reading proofs.