Graph Terminology


A path is a sequence of consecutive edges in a graph.

Alternatively, we can define “path” as a sequence of vertices where each vertex in the sequence is adjacent to the vertex next to it.

Consider the following graph:

Here are two pathes from $A$ to $C$: $(A, C)$ and $(A, B, D, C)$.

A simple path is a path that does not repeat any nodes or edges.

In this class, when I say “path”, I mean “simple path”.

Aside: In some references, what I defined as “path” is defined as “walk” and instead “simple path” is called, simply, “path”.

Exercise List the edges on a directed path from $B$ to $E$ and from $C$ to $E$.

  • Directed path from $B$ to $E$: $((B, D), (D, E))$.
  • There is no directed path from $C$ to $E$.