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 [1]. 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 [1] 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

[1] (1,2)

https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29#Bridge-Finding_with_Chain_Decompositions

Examples

The barbell graph with parameter zero has a single bridge:

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