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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 )).
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
The graph on the upper left can be strongly oriented, as shown by the lower left graph which is strongly connected. The lower right is an orientation of the upper right graph, but not a strong one. In graph theory , a strong orientation of an undirected graph is an assignment of a direction to each edge (an orientation ) that makes it into a ...
A directed graph is weakly connected (or just connected [9]) if the undirected underlying graph obtained by replacing all directed edges of the graph with undirected edges is a connected graph. A directed graph is strongly connected or strong if it contains a directed path from x to y (and from y to x) for every pair of vertices (x, y). The ...
In graph theory, Robbins' theorem, named after Herbert Robbins (), states that the graphs that have strong orientations are exactly the 2-edge-connected graphs.That is, it is possible to choose a direction for each edge of an undirected graph G, turning it into a directed graph that has a path from every vertex to every other vertex, if and only if G is connected and has no bridge.
Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time , matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm .
Similarly, a strict partial order that is connected is a strict total order. A relation is a total order if and only if it is both a partial order and strongly connected. A relation is a strict total order if, and only if, it is a strict partial order and just connected. A strict total order can never be strongly connected (except on an empty ...
5. A strongly perfect graph is a graph in which every induced subgraph has an independent set meeting all maximal cliques. The Meyniel graphs are also called "very strongly perfect graphs" because in them, every vertex belongs to such an independent set. subforest A subgraph of a forest. subgraph