In general, a walk is an alternating sequence of vertices and edges, as
defined in df-wlks: p(0) e(f(1)) p(1) e(f(2)) ... p(n-1) e(f(n)) p(n).
Often, it is sufficient to refer to a walk by the natural sequence of its
vertices, i.e omitting its edges in its representation: p(0) p(1) ... p(n-1)
p(n), see the corresponding remark in [Diestel] p. 6. The concept of a
, see df-word, is the appropriate way to define such a sequence
(being finite and starting at index 0) of vertices. Therefore, it is used in
definitions df-wwlks and df-wwlksn, and the representation of a walk as
sequence of its vertices is called "walk as word".
Only for simple pseudographs, however, the edges can be uniquely
reconstructed from such a representation. In other cases, there could be
more than one edge between two adjacent vertices in the walk (in a
multigraph), or two adjacent vertices could be connected by two different
hyperedges involving additional vertices (in a hypergraph).