A path in a graph is a finite sequencePlanetmathPlanetmath of alternating vertices and edges, beginning and ending with a vertex, v1e1v2e2v3en-1vn such that every consecutive pair of vertices vx and vx+1 are adjacent and ex is incidentPlanetmathPlanetmath with vx and with vx+1. Typically, the edges may be omitted when writing a path (e.g., v1v2v3vn) since only one edge of a graph may connect two adjacent vertices. In a multigraphMathworldPlanetmath, however, the choice of edge may be significant.

The length of a path is the number of edges in it.

Consider the following graph:


Paths include (but are certainly not limited to) ABCD (length 3), ABCDA (length 4), and ABABABABADCBA (length 12). ABD is not a path since B is not adjacent to D.

In a digraphMathworldPlanetmath, each consecutive pair of vertices must be connectedPlanetmathPlanetmath by an edge with the proper orientationPlanetmathPlanetmath; if e=(u,v) is an edge, but (v,u) is not, then uev is a valid path but veu is not.

Consider this digraph:


GHIJ, GJ, and GHGHGH are all valid paths. GHJ is not a valid path because H and J are not connected. GJI is not a valid path because the edge connecting I to J has the opposite orientation.

Title path
Canonical name Path1
Date of creation 2013-03-22 12:16:49
Last modified on 2013-03-22 12:16:49
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Definition
Classification msc 05C38
Related topic ClosedPath
Defines path length