Formal definition
Let \(G = (V, A_G)\) be a graph (or digraph), where \(V\) is the set of vertices and \(A_G \subseteq V \times V\) is the set of edges (or arcs).
A walk in \(G\) is any sequence of vertices \((s_0, s_1, \ldots, s_k)\) such that each consecutive pair is an edge of the graph:
We say that this walk has length \(k\), starts at \(s_0\), and ends at \(s_k\). Note that a walk may repeat vertices and edges.
Intuition
Think of a walk as “following arrows/edges” step by step: at each move you go from \(s_i\) to \(s_{i+1}\) using an edge that exists in the graph.
Example
If \((A,C)\in A_G\) and \((C,D)\in A_G\), then \((A,C,D)\) is a walk of length \(2\).