Root material that has been dug up then ejected some metres beyond the site, generating several more plants...
The uninformed distribution of this single piece of surface root crown has generated at least 3 whole new plants... however, the fine and hairlike smaller root systems are extensive, and spread at a much deeper level than visibly apparent.
Under-estimating the plant's vigour, persistence and rate of spread will enable establishment of knotweed with the same voracity as, say, deliberately planting it, fly-tipping or dumping its waste in a watercourse.
Negligence (rather than deliberation or malice of course) coupled with ignorance are thus primary vectors of spread, if you like.