This project is aimed at providing linear time implementation for modular decomposition of graphs and digraphs. Modular decomposition is decomposition of graph into modules. A module is a subset of vertices and it is a generalization of connected component in graph. Let us take for example a module X. For any vertex v ∉ X it is either connected or not connected to every vertex of X. Another property of module is that a module can be subset of another module. There are various algorithms which have been published for modular decomposition of graphs. The focus in this project is on linear time complexity algorithms which can be practically implemented. The project further aims to use the modules developed for modular decomposition to implement other functionality like skew partitions. Skew partition is partition of graph into two sets of vertices such that induced graph formed by one set is disconnected and induced graph formed by other set is complement of the first. Modular decomposition is a very important concept in Graph Theory and it has a number of use cases. For instance it has been an important tool for solving optimization and combinatorics problems.


Lokesh Jain


  • Dima Pasechnik