Directed path - Knowlpedia

A directed path of length $k$ in a directed graph is a sequence $v_0,\ldots,v_k$ with $v_{j-1}\to v_j$ for $1\le j\le k$ . A length-zero path consists of a single vertex.

Convention and reachability

Here repeated vertices are permitted; some texts call this a directed walk and reserve “path” for sequences with no repeated vertices. A path with no repeated vertices is called simple. A vertex $v$ is reachable from $u$ if a directed path starts at $u$ and ends at $v$ . Paths with matching endpoints can be concatenated.