Setting random means each graph model starts with randomly placed vertices. Setting biased means we feed Fruchterman-Reingold with initial random placement, then feed that output into the input of node linlog, then feed that output into the input of edge linlog.
You can toggle whether or not edges are shown by pressing 'e' (not shown by default). You can toggle whether or not vertex labels are shown by pressing 'l' (not shown by default, and not recommended for large graphs unless you're zoomed in (future feature)).
The Linlog energy models show clear clusters of vertices. One algorithm one could apply to actually assign cluster numbers to vertices is -means. Note that both Linlog and -means have the potential to suffer from poor local solutions. The paper also briefly mentions extensions of this algorithm to compute clustering assignments (which involve computing barycenters — not too far off from the ideas of -means).