Return a generator of articulation points, or cut vertices, of a graph.
An articulation point or cut vertex is any node whose removal (along with
all its incident edges) increases the number of connected components of
a graph. An undirected connected graph without articulation points is
biconnected. Articulation points belong to more than one biconnected
component of a graph.
Notice that by convention a dyad is considered a biconnected component.
Parameters : | G : NetworkX Graph
|
Returns : | articulation points : generator
|
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
[R161] | 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
>>> list(nx.articulation_points(G))
[6, 5, 4, 3]
>>> G.add_edge(2,8)
>>> print(nx.is_biconnected(G))
True
>>> list(nx.articulation_points(G))
[]