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.
There are variants of modular decomposition for undirected graphs and directed graphs. For each undirected graph, this decomposition is unique.
This notion can be generalized to other structures (for example directed graphs) and is useful to design efficient algorithms for the recognition of some graph classes, for finding transitive orientations of comparability graphs, for optimization problems on graphs, and for graph drawing.
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In graph theory, the modulardecomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected...
by decomposition into smaller pieces, and all originating around the 1960s. While the historical usage of these terms has been inconsistent, "modular programming"...
module or modular in Wiktionary, the free dictionary. Module, modular and modularity may refer to the concept of modularity. They may also refer to: Modular design...
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety...
(up to permutation symmetry) if it is prime with respect to the modulardecomposition. If ρ = ( σ 1 , σ 2 , . . . , σ n ) {\displaystyle \rho =(\sigma...
Modular design, or modularity in design, is a design principle that subdivides a system into smaller parts called modules (such as modular process skids)...
to shortest paths between all pairs of the triple. 2. Modulardecomposition, a decomposition of a graph into subgraphs within which all vertices connect...
inference, hierarchical clustering, and quadtree decomposition are all examples of function decomposition. Many statistical inference methods can be thought...
In mathematics, and in particular modular representation theory, a decomposition matrix is a matrix that results from writing the irreducible ordinary...
Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups...
strong perfect graph theorem. A homogeneous pair is related to a modulardecomposition of a graph. It is a partition of the graph into three subsets V1...
Pyrolysis is the process of thermal decomposition of materials at elevated temperatures, often in an inert atmosphere. The word pyrolysis is coined from...
in computer science) In number theory, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer...
Modularity of mind is the notion that a mind may, at least in part, be composed of innate neural structures or mental modules which have distinct, established...
cotree representation constructed, using modulardecomposition, partition refinement, LexBFS , or split decomposition. Once a cotree representation has been...
shortened by replacing the usual triangular decomposition of the Monster Lie algebra with a decomposition into a sum of gl2 and two free Lie algebras...
methanol); and to produce hydrogen and oxygen by decomposing water thermochemically. The PBMR is modular in that only small to mid-sized units will be designed...
radiation has not been commercialized. Electrolysis of water is the decomposition of water (H2O) into oxygen (O2) and hydrogen (H2): Production of hydrogen...
theorem it decomposes as a direct product of matrix rings. The Fourier transform on finite groups explicitly exhibits this decomposition, with a matrix...
complementary representation). The decomposition of a semisimple representation into simple ones, called a semisimple decomposition, need not be unique; for example...
model may indeed be analyzed at this top level of modulardecomposition, we need to further decompose basal ganglia, BG, as shown in Figure 3(c) if we...
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