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 strong module is a graph module that does not overlap another graph module, where two sets overlap when their intersection and both set differences are nonempty. The strong graph modules form the nodes of the modular decomposition tree.
Every singleton set and the full vertex set are graph modules. A class of twin vertices is also a graph module, but a graph module need not consist of pairwise twins.
