A graph module of a graph 
is a vertex set 
such that every vertex outside 
is adjacent either to every vertex in 
or to no vertex in 
. Equivalently, vertices in 
have identical neighbors outside 
.
A module is strong if it does not overlap another module, where two sets overlap when their intersection and both set differences are nonempty. The strong modules form the nodes of the modular decomposition tree.
Every singleton and the full vertex set are modules. A class of twin vertices is also a module, but a module need not consist of pairwise twins.
