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, an edge is a bridge if and only if it is not contained in any cycle. For a connected graph, a bridge can uniquely determine a cut. A graph is said to be bridgeless or isthmus-free if it contains no bridges.

This type of bridge should be distinguished from an unrelated meaning of "bridge" in graph theory, a subgraph separated from the rest of the graph by a specified subset of vertices; see bridge.