Is there any term for denoting two vertices that are adjacent to the same node?

Question

Let $G = (V,E)$ be a graph with $V = \{a, b, c\}$ and $E = \{(a,b), (b,c)\}$. That is, vertex $a$ and vertex $c$ are adjacent to the vertex $b$. Is there any formal way to refer to the relation between vertices $a$ and $c$ ?

Answer 1

We can define $B(v,r)=\{u|\operatorname{dist}(u,v)\le r\}$, where $u,v$ are vertices of a graph $G$, and $r$ is the number of edges traversable.

Then your $a,c$ belong to $B(b,1)$.

Answer 2

One way of describing such a relation is by saying that $a$ and $c$ belong to the $1$-degree neighborhood of vertex $b$. Alternatively, vertices $a$ and $c$ are exactly $2$ hops away from one another: $c$ belongs to the $2$-degree neighborhood of $a$.

Answer 3

You can say that $a$ and $c$ share a neighbor.

I hope this helps $\ddot\smile$