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Strongly connected component information


Graph with strongly connected components marked

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 connected components of a directed graph form a partition into subgraphs that are themselves strongly connected. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(V + E )).

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Strongly connected component

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are themselves strongly connected. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time...

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Component

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Identity component Irreducible component Spare part Strongly connected component Tangential and normal components Category:Components This disambiguation page...

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Connected space

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collection of connected subsets such that each contained x {\displaystyle x} will once again be a connected subset. The connected component of a point x...

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Weak component

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weak components were defined in a 1972 paper by Ronald Graham, Donald Knuth, and (posthumously) Theodore Motzkin, by analogy to the strongly connected components...

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Connectedness

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simply connected small-world network strongly connected component totally disconnected "the definition of connectedness". Dictionary.com. Retrieved 2016-06-15...

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Biconnected graph

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biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected...

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Eulerian path

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and all of its vertices with nonzero degree belong to a single strongly connected component. Equivalently, a directed graph has an Eulerian cycle if and...

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Feedback arc set

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strongly connected component of the given graph, and to break these strongly connected components down even farther to their biconnected components by...

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Directed acyclic graph

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a DAG, called its condensation, by contracting each of its strongly connected components into a single supervertex. When the graph is already acyclic...

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Transitive reduction

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where X and Y are two strongly connected components of G that are connected by an edge in the condensation, x is any vertex in component X, and y is any vertex...

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Glossary of graph theory

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and strongly connected components of directed graphs, see connected and component. A strong orientation is an orientation that is strongly connected; see...

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Quotient graph

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Harold N.; Somenzi, Fabio (January 2006), "An algorithm for strongly connected component analysis in n log n symbolic steps", Formal Methods in System...

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Pixel connectivity

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q_{i}\in \{0,1,...,k\},\forall i\in \{1,2,...,N\}} and that at least one component q i = k {\displaystyle q_{i}=k} Let S N d {\displaystyle S_{N}^{d}} represent...

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Locally connected space

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connected if every point admits a neighbourhood basis consisting of open connected sets. As a stronger notion, the space X is locally path connected if...

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Vertex separator

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the removal of S from the graph separates a and b into distinct connected components. Consider a grid graph with r rows and c columns; the total number...

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Aperiodic graph

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not strongly connected, we may perform a similar computation in each strongly connected component of G, ignoring the edges that pass from one strongly connected...

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Link farm

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website linking Scraper site Server farm Spam blog Spam in blogs Strongly connected component Web guide "link farming". www.webopedia.com. 16 January 2002...

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SCC

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Controller Single-chip Cloud Computer, Intel's 48-core research chip Strongly connected component in graph theory Suncoast Conference South Central Conference...

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Topological sorting

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sorted Tarjan's strongly connected components algorithm, an algorithm that gives the topologically sorted list of strongly connected components in a graph...

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List of graph theory topics

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switching game Spectral graph theory Spring-based algorithm Strongly connected component Vertex cover problem See list of network theory topics Helly...

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Robert Tarjan

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discoverer of several graph theory algorithms, including his strongly connected components algorithm, and co-inventor of both splay trees and Fibonacci...

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