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 on 
vertices, the diamond graph,
empty graphs, and the singleton
graph.
A connected graph on at least two vertices is bridgeless iff it is 2-edge-connected.
It can be tested for being bridgeless 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 unlabeled simple bridgeless graphs on 
,
2, ... vertices are 1, 1, 2, 5, 16, 77, 582, 8002,
... (OEIS A263914).
The numbers of unlabeled simple connected bridgeless graphs on 
, 2, ... vertices are 1,
0, 1, 3, 11, 60, 502, 7403, ... (OEIS A007146).
