Live briefing
Everything about Modular decomposition
Recursively splitting a graph into subsets of nodes
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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Modular decompositionA 5-minute orientation
- Skim a recent paper: Modulation of Co spin state at Co3O4 crystalline-amorphous interfaces for CO oxidation and N2O decompositionInfluential work since 2022
- Pick up a classic book: Decompositions in lattices and some representations of algebrasThe most-reprinted book on the subject
- Read the landmark paper: Modular decomposition and transitive orientationCited 287 times
- Go sideways: Split (graph theory)A closely related topic
- Go sideways: Glossary of graph theoryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Modular decomposition and transitive orientation
Modular decomposition in visuomotor learning
A survey of the algorithmic aspects of modular decomposition
Modular decomposition of protein-protein interaction networks
Incremental modular decomposition
Linear-time modular decomposition of directed graphs
Applying Modular Decomposition to Parameterized Cluster Editing Problems
Efficient and Practical Algorithms for Sequential Modular Decomposition
🆕 Influential since 2022
Modulation of Co spin state at Co3O4 crystalline-amorphous interfaces for CO oxidation and N2O decomposition
Fault diagnosis of modular multilevel converter based on adaptive chirp mode decomposition and temporal convolutional network
A self-organizing modular neural network based on empirical mode decomposition with sliding window for time series prediction
A pseudo-inverse decomposition-based self-organizing modular echo state network for time series prediction
From modular decomposition trees to rooted median graphs
📚 Books worth reading
- 📕Decompositions in lattices and some representations of algebrasAndrzej Walendziak · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Split (graph theory) In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits…
- Glossary of graph theory Look up Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs,…
- Strongly connected component In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly…
- Gallai–Edmonds decomposition In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure…
- Bridge (graph theory) In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. Equivalently…
- Factor-critical graph In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph) is a graph with an odd number of vertices in which deleting…
- Dulmage–Mendelsohn decomposition In graph theory, the Dulmage–Mendelsohn decomposition is a partition of the vertices of a bipartite graph into subsets, with the property that two adjacent…
- Planar separator theorem In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into…