# bridges#

bridges(G, root=None)[source]#

Generate all bridges in a graph.

A bridge in a graph is an edge whose removal causes the number of connected components of the graph to increase. Equivalently, a bridge is an edge that does not belong to any cycle. Bridges are also known as cut-edges, isthmuses, or cut arcs.

Parameters:
Gundirected graph
rootnode (optional)

A node in the graph G. If specified, only the bridges in the connected component containing this node will be returned.

Yields:
eedge

An edge in the graph whose removal disconnects the graph (or causes the number of connected components to increase).

Raises:
NodeNotFound

If root is not in the graph G.

NetworkXNotImplemented

If G is a directed graph.

Notes

This is an implementation of the algorithm described in . An edge is a bridge if and only if it is not contained in any chain. Chains are found using the networkx.chain_decomposition() function.

The algorithm described in  requires a simple graph. If the provided graph is a multigraph, we convert it to a simple graph and verify that any bridges discovered by the chain decomposition algorithm are not multi-edges.

Ignoring polylogarithmic factors, the worst-case time complexity is the same as the networkx.chain_decomposition() function, $$O(m + n)$$, where $$n$$ is the number of nodes in the graph and $$m$$ is the number of edges.

References

Examples

The barbell graph with parameter zero has a single bridge:

>>> G = nx.barbell_graph(10, 0)
>>> list(nx.bridges(G))
[(9, 10)]