Why this page says module where some sources say homogeneous set

The target paper uses the phrase homogeneous set for what this page calls a module. This library already uses homogeneous set at order 395 for a clique or a stable set, through the homogeneous number $\mathrm{hom}(G)$ (Homogeneous vertex sets and the homogeneous number $\mathrm{hom}(G)=\max \{\omega (G),\alpha (G)\}$), so reusing the same words here would create an avoidable ambiguity inside the same graph-theory block.

Harju writes clan and explicitly notes that it is the same object as a module. His notes-on-references list the wider synonym family: closed set (Gallai), autonomous set, partitive set, externally related set, condensible set, homogeneous set, interval, and module. The present page adopts Habib and Paul's word module because it is standard and does not collide with the already-published meaning of homogeneous set.