A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include
complete graphs on 
nodes, cycle graphs, the
diamond graph, empty
graphs, and the singleton graph.
Connected bridgeless graphs are 2-edge connected and can be tested for in the Wolfram Language using KEdgeConnectedGraphQ[g,
2] or EdgeConnectivity[g]
.
A graph that is not bridgeless is said to be bridged.
The numbers of simple bridgeless graphs on 
, 2, ... vertices are 1, 1, 2, 5, 16, 77, 582, 8002, ...
(OEIS A263914).
The numbers of simple connected bridgeless graphs on 
, 2, ... vertices are 1, 0, 1, 3, 11, 60, 502, 7403 ... (OEIS
A007146).
