This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.


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.

  • 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.

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


NodeNotFound – If root is not in the graph G.


The barbell graph with parameter zero has a single bridge:

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


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.