There are various methods to decompose coloured graphs.
Decompositions of combinatorial and algebraic structures
are special cases of the divide-and-conquer method,
where a large problem is partitioned into smaller ones,
and a method is given to link solutions of the subproblems to
a solution of the original one.
The clan decomposition
(modular or substitution decomposition),
is a structural result on general graphs related to the decomposition by quotients in algebra.
The lectures are divided into a `static' and 'dynamic' parts.
The static part is concerned with
the decomposability and primitivity.
The key notion is that of a clan -
a subset of vertices that cannot be distinguished from each other by
The `dynamic' part studies the local transformation of switching.
The set of labels of the edges is given a group structure.
In this way one obtains switching classes of graphs.