Bridges in Graph

In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases its number of connected components. Equivalently, an edge is a bridge if and only if it is not contained in any cycle. A graph is said to be bridgeless or isthmus-free if it contains no bridges.

A graph with 16 vertices and 6 bridges (highlighted in red)

An undirected connected graph with no cut edges