Walks, closed walks, trails, paths and cycles, with length equal to the number of traversed edges

Let $G=(V,E)$ be a graph. A walk of length $\ell$ is a finite vertex list

$W=(v_0,v_1,\ldots,v_\ell)$

such that $\{v_{i-1},v_i\}\in E$ for every $1\le i\le\ell$. Its endpoints are $v_0$ and $v_\ell$. The length is the number $\ell$ of traversed edges, not the number of displayed vertices. A walk is closed when $v_0=v_\ell$.

A trail is a walk in which the traversed edges are distinct. A path is a walk in which the vertices are distinct. In particular, $(v)$ is a path of length $0$ from $v$ to itself.

A cycle is a closed walk $(v_0,\ldots,v_{\ell-1},v_\ell=v_0)$ of length $\ell\ge3$ in which $v_0,\ldots,v_{\ell-1}$ are distinct. A graph is acyclic when it contains no cycle. Reversing any walk, trail, path, or cycle preserves its type and length.