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A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. 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. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
Several algorithms based on depth-first search compute strongly connected components in linear time.. Kosaraju's algorithm uses two passes of depth-first search. The first, in the original graph, is used to choose the order in which the outer loop of the second depth-first search tests vertices for having been visited already and recursively explores them if not.
The unification of two argument graphs is defined as the most general graph (or the computation thereof) that is consistent with (i.e. contains all of the information in) the inputs, if such a graph exists; efficient unification algorithms are known.
A graph G which is connected but not 2-connected is sometimes called separable. Analogous concepts can be defined for edges. In the simple case in which cutting a single, specific edge would disconnect the graph, that edge is called a bridge. More generally, an edge cut of G is a set of edges whose removal renders the graph disconnected.
Since, at most, two land masses can serve as the endpoints of a walk, the proposition of a walk traversing each bridge once leads to a contradiction. In modern language, Euler shows that the possibility of a walk through a graph, traversing each edge exactly once, depends on the degrees of the nodes. The degree of a node is the number of edges ...
Download as PDF; Printable version; ... Bridge (graph theory) C. Component (graph theory) ... Stoer–Wagner algorithm; Strength of a graph;
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 .
An extension of Robbins' theorem to mixed graphs by Boesch & Tindell (1980) shows that, if G is a graph in which some edges may be directed and others undirected, and G contains a path respecting the edge orientations from every vertex to every other vertex, then any undirected edge of G that is not a bridge may be made directed without changing the connectivity of G.