I was just brushing up on my discrete mathematics specifically graph theory and read the following definition of a walk in a graph
"A walk in a graph is an alternating sequence of vertices and edges from a start vertex to an end vertex where start and the end vertices are not necessarily distinct"
and after this I read up the definition of a path in a graph which says
"A path in a graph is a walk in the graph with no repeated vertices"
the point of confusion is that the definition for a path doesn't mention anything about the repetition of edges in a path, although the idea of repetition of edge in a path sounds absurd to me because that eventually means that I am taking the same road that I traversed previously and hence repeating the same destinations which are the vertices respectively. I am curious to know if there is any such case of a path where there is a repetitive edge but no repeated vertex.
One more thing I would like to know is can there exists an ordering of edges in a graph such that the path from one vertex to another is infinite in short can there be an infinite path in a finite graph?