Graph Terminology I

Adjacency

For an edge $e = (u, v)$ that connects node $u$ to node $v$, we say that $v$ is adjacent to $u$, or that $v$ is a neighbor of $u$. The edge $e$ is called incident to both $u$ and $v$.

The number of neighbors of a node $v$ is called the degree of $v$, written deg($v$).

In the following example graph, $c$ is a neighbor of $b$, as there is an edge $(b, c)$. But $b$ is not a neighbor of $c$, as there is no edge $(c, b)$. The degree of node $a$ is deg$(a) = 2$, as it has two neighbors.