Unrooted softwired distance

[lutteropp]

@celinescornavacca I've read the part in your book about hardwired/softwired clusters in rooted phylogenetic networks. Now I understand what these are:

• A cluster induced by an edge is the set of taxa descending from the target node of the edge.
• For hardwired clusters, we keep all reticulation edges activated at once, and each edge induces a single cluster this way.
• For softwired clusters, we go through the displayed trees one-by-one, switching reticulation edges on and off during the process. Here, each edge induces a set of clusters (up to one per displayed tree).

You mentioned that for softwired network distance, we can modify its definition by treating the displayed trees as unrooted ones. My question is here: How is a cluster defined in an unrooted tree, where the edges have no direction? Which side of the bipartition induced by the edge is the cluster then?