Return a generator of sets of nodes, one set for each biconnected
component of the graph
Biconnected components are maximal subgraphs such that the removal of a
node (and all edges incident on that node) will not disconnect the
subgraph. Note that nodes may be part of more than one biconnected
component. Those nodes are articulation points, or cut vertices. The
removal of articulation points will increase the number of connected
components of the graph.
Notice that by convention a dyad is considered a biconnected component.
Parameters : | G : NetworkX Graph
|
Returns : | nodes : generator
Generator of sets of nodes, one set for each biconnected component.
|
Raises : | NetworkXError : :
If the input graph is not undirected.
|
Notes
The algorithm to find articulation points and biconnected
components is implemented using a non-recursive depth-first-search
(DFS) that keeps track of the highest level that back edges reach
in the DFS tree. A node
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is an articulation point if, and only
if, there exists a subtree rooted at
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such that there is no
back edge from any successor of
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in the DFS tree. By keeping track of all the edges traversed
by the DFS we can obtain the biconnected components because all
edges of a bicomponent will be traversed consecutively between
articulation points.
References
[R164] | Hopcroft, J.; Tarjan, R. (1973).
“Efficient algorithms for graph manipulation”.
Communications of the ACM 16: 372–378. doi:10.1145/362248.362272 |
Examples
>>> G = nx.barbell_graph(4,2)
>>> print(nx.is_biconnected(G))
False
>>> components = nx.biconnected_components(G)
>>> G.add_edge(2,8)
>>> print(nx.is_biconnected(G))
True
>>> components = nx.biconnected_components(G)