Reachability

Definition

Let $G$ be a graph and let $u, v$ be vertices of $G$. The vertex $v$ is reachable from $u$ if there is a walk in $G$ from $u$ to $v$.

Remarks

Reachability is an equivalence relation on the vertices. It is reflexive by the walk of length $0$, symmetric by reversal of a walk, and transitive by concatenation. Its equivalence classes are the connected components of $G$. For a directed graph, reachability along arcs is reflexive and transitive, but in general it is not symmetric.

Explanations

L1 human

A vertex is reachable from another one when you can go from the first to the second along edges. On a map of islands with bridges, two places are reachable from each other when they are on islands linked by bridges.