I'll start with the clarification that the moderators have changed the URL of the original post from <https://susam.net/no-query-strings.html> to <https://chrismorgan.info/no-query-strings>. Hopefully, this will prevent any confusion about why we are discussing random walks in a post about query strings. Now let me answer your question.

> Is it not a random walk? Might sound pedantic but if there is graph structure I am interested.

The network is a directed graph. Every Wander Console declares a few other consoles as its neighbours. The person setting up the console decides who they want to list as their neighbours. So if we call the network graph X, then the set of vertices is:

  V(X) = the set of all URLs that point to Wander Consoles

  E(X) = {(u, v) in V(X) : u declares v as its neighbour}

The difference from a random walk is that the next console is not chosen from the neighbours of the last visited console. It is chosen from the whole set of consoles discovered so far. In other words, each click expands the known part of the graph, but the console used for that expansion is selected randomly from all discovered consoles, not just from the last console visited.