networkx.algorithms.bridges.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.

Parameters

G (undirected graph)
root (node (optional)) – A node in the graph G. If specified, only the bridges in the connected component containing this node will be returned.

Yields

e (edge) – 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.

Examples

The barbell graph with parameter zero has a single bridge:

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

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.

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