Can the clusterings returned by mcl contain overlap?
No. Clusterings resulting from the abstract MCL algorithm may in theory contain overlap, but the default behaviour in mcl is to remove it should it occur, by allocating the nodes in overlap to the first cluster in which they are seen. mcl will warn you if this occurs. This behaviour is switched off by supplying –keep-overlap=yes. Do note that overlap is mostly a theoretical possibility. It is conjectured that it requires the presence of very strong symmetries in the input graph, to the extent that there exists an automorphism of the input graph mapping the overlapping part onto itself. It is possible to construct (highly symmetric) input graphs leading to cluster overlap. Examples of overlap in which a few nodes are involved are easy to construct; examples with many nodes are exceptionally hard to construct. Clusterings associated with intermediate/early MCL iterands may very well contain overlap, see the introduction in this section and other entries.
