What is the “distance” of a random walk on a graph?

What is the definition of the distance of a random walk? In the Statistical significance of a cluster of this paper, and this blog, they both mention the distance of a random walk.

I think it should be a different concept from the length of a random walk.

• it would help if your title mentioned that you're talking about the random walks on graphs, it's very different from an ordinary RW. in this case your papers mean by distance is the length of a walk on a graph as measured by edges walked – Aksakal Feb 27 '18 at 16:08
• @Aksakal But in the blog with visualization, clearly length and distance are two different quantities. – user3813057 Feb 27 '18 at 22:08