Modular decomposition
![A graph, its quotient where](/Images/godic/202501/27/ModularDecomposition0231.png")
![An O(n) representation of the modular decomposition](/Images/godic/202501/27/page1-220px-O_n_ModularDecompRep.pdf0231.jpg")
![The modular decomposition, augmented with a quotient on the children of each internal node, gives a complete representation of G.](/Images/godic/202501/27/page1-220px-ModDecompQuotients.pdf0231.jpg")
In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can be a proper subset of another. Modules therefore lead to a recursive (hierarchical) decomposition of the graph, instead of just a partition.