In graph theory, a **bridge** (also known as a **cut-edge**) is an edge in a connected graph whose removal increases the number of connected components of the graph. In simpler terms, a bridge is an edge that, when deleted, disconnects the graph, effectively separating it into two or more disjoint parts. Bridges are important in network design and reliability analysis because they represent critical connections whose failure would fragment the network.
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A bridge is an edge whose deletion increases the number of components of a graph. Equivalently, it belongs to no cycle; within its original component, deleting it makes the connected graph disconnected.