> [!NOTE] Definition (Path) > A [[Walk in Undirected Graph|walk]] that does not use the same edge vertex than once is *path* > > We may also define a path $P_{n}$ as [[Graphs|graph]] on $n$ nodes $v_{1},\dots,v_{n}$ with edge-set $\{ (v_{i}, v_{i+1}) \mid 1 \leq i \leq n-1 \}.$ # Properties A [[Hamiltonian Path|hamiltonian]] path of $G$ is a path induced on all vertices of $G.$ The *length* of a path is defined as the number of edges in it. The shortest path between two vertices is the path with lowest length. The [[Shortest Path Problem|problem of finding a shortest path]] is a computational one. # Applications - [[Cycle (Type of Simple Graph)]]. - [[Shortest Path Problem]].