Definition

A path is a Graph where the edges have a certain length.

Denoted as $P_{n}$ , a graph with path length $n$ .
If vertices are $v_{1}, \dots, v_{n}$ then the edges are $(v_{1}, v_{2}), \dots (v_{n - 1}, v_{n})$
$∣ E ∣ = n - 1$

graph LR
    A((A)) o--o B((B))
    B o--o C((C))
    C o--o D((D))

A path is a Walk with no repeated vertices.